Substructures in large graphs and hypergraphs
Lead Research Organisation:
London School of Economics and Political Science
Department Name: Mathematics
Abstract
In this project, we seek to understand the fundamental mathematical properties of discrete structures. In particular, we study graphs, which are collections of vertices, together with a set of unordered pairs of vertices called edges. Graphs are used to model transportation networks, social networks, large data sets, and more, and as such, a deeper understanding of their fundamental properties is beneficial to a wide variety of their applications.
This project falls within the area of Extremal Graph Theory, in which one major direction concerns the minima and maxima of graph parameters among graphs avoiding a certain substructure. This project considers this type of problems, where the substructure is a large set of edge-disjoint or vertex-disjoint copies of a prescribed small or sparse graph; these are known in the area as packing and tiling problems, respectively. For example, part of this project seeks to understand what is the maximum number of triangles which can be packed edge-disjointly in a graph with a given density of edges.
A second part of this project concerns a well-known conjecture of Jackson (c. 1980) on packing Hamilton cycles in bipartite oriented graphs. An oriented graph is obtained from a graph by specifying an orientation for each edge, and a Hamilton cycle is a cyclic ordering of the vertices such that every two consecutive vertices are connected by an edge. It was recently shown that every regular orientation of the complete graph can be decomposed into such Hamilton cycles. We seek to prove Jackson's conjecture, which is a natural bipartite analogue of this result, as well as investigate a related conjecture of Kuhn and Osthus on tripartite graphs.
Finally, a significant portion of this project is dedicated to investigating the maximum edge-density in a uniformly dense hypergraph which avoids a fixed subhypergraph. Hypegraphs are a natural generalisation of graphs, which allows for the modelling of relationships among more than two objects. In particular, their edge set consists of subsets of vertices whose size is not necessarily two. We seek to understand, in a certain family of pseudorandom hypegraphs, what edge density forces the emergence of a given subhypergraph.
This project falls within the area of Extremal Graph Theory, in which one major direction concerns the minima and maxima of graph parameters among graphs avoiding a certain substructure. This project considers this type of problems, where the substructure is a large set of edge-disjoint or vertex-disjoint copies of a prescribed small or sparse graph; these are known in the area as packing and tiling problems, respectively. For example, part of this project seeks to understand what is the maximum number of triangles which can be packed edge-disjointly in a graph with a given density of edges.
A second part of this project concerns a well-known conjecture of Jackson (c. 1980) on packing Hamilton cycles in bipartite oriented graphs. An oriented graph is obtained from a graph by specifying an orientation for each edge, and a Hamilton cycle is a cyclic ordering of the vertices such that every two consecutive vertices are connected by an edge. It was recently shown that every regular orientation of the complete graph can be decomposed into such Hamilton cycles. We seek to prove Jackson's conjecture, which is a natural bipartite analogue of this result, as well as investigate a related conjecture of Kuhn and Osthus on tripartite graphs.
Finally, a significant portion of this project is dedicated to investigating the maximum edge-density in a uniformly dense hypergraph which avoids a fixed subhypergraph. Hypegraphs are a natural generalisation of graphs, which allows for the modelling of relationships among more than two objects. In particular, their edge set consists of subsets of vertices whose size is not necessarily two. We seek to understand, in a certain family of pseudorandom hypegraphs, what edge density forces the emergence of a given subhypergraph.
Organisations
- London School of Economics and Political Science (Fellow, Lead Research Organisation)
- UNIVERSITY OF OXFORD (Collaboration)
- QUEEN MARY UNIVERSITY OF LONDON (Collaboration)
- London School of Economics and Political Science (University of London) (Collaboration)
- Universidade de São Paulo (Collaboration)
- ETH Zurich (Collaboration)
- University of California, Irvine (Collaboration)
- Hamburg University of Technology (Collaboration)
- The Open University (Collaboration)
- University of Warwick (Collaboration)
- Polytechnic University of Catalonia (Collaboration)
Publications
Bowtell Candida
(2023)
Universality for transversal Hamilton cycles
in arXiv e-prints
Pehova Yanitsa
(2023)
Embedding loose spanning trees in 3-uniform hypergraphs
in arXiv e-prints
| Description | The work funded through this award has produced several academic papers which have either been submitted to top journals or are in final stages of preparation (https://arxiv.org/abs/2310.04138, https://arxiv.org/abs/2301.09630). The focus of each paper is the proof of one or several related theoretical results from pure mathematics. The main topic of the project is Graph Theory which is the theoretical study of networks. Each result constitutes an answer to a theoretical question that relates local and global properties of large networks. |
| Exploitation Route | The ideas developed in the academic papers due to be published are disseminated to other researchers from the area, who can apply them to their own research. The results of this project contribute to the theoretical knowledge base on the behaviour of large networks, which is the main building block for future applications. |
| Sectors | Digital/Communication/Information Technologies (including Software) Financial Services and Management Consultancy |
| URL | https://sites.google.com/site/yanitsapehova/ |
| Description | Marie Sklodowska Curie Actions - Postdoctoral Fellowship (Global) |
| Amount | € 255,043 (EUR) |
| Funding ID | GAP-101154650 |
| Organisation | European Commission |
| Sector | Public |
| Country | European Union (EU) |
| Start | 08/2024 |
| End | 02/2027 |
| Description | Research collaboration with Asaf Ferber, Mason Shurman and Marcelo Sales (University of California Irvine) |
| Organisation | University of California, Irvine |
| Country | United States |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint work on project "Covering random digraphs with Hamilton cycles". This project was initiated during a 2-week research visit of the PI to University of California Irvine. |
| Collaborator Contribution | Prof Asaf Ferber, Mason Shurman and Marcelo Sales (University of California Irvine) contributed to joint work on project "Covering random digraphs with Hamilton cycles". Prof Asaf Ferber proposed the project, which extends hos previous work. |
| Impact | We initiated work on Hamilton cycle covers of the random directed graph D(n,p) using a number of cycles exactly equal to the (observed) maximum degree of the dirgraph. This extends previous work of Prof Ferber but requires new ideas to work in the directed setting. The problem is motivated by open problems on the chromatic index of random hypergraphs. |
| Start Year | 2023 |
| Description | Research collaboration with Candy Bowtell (Warwick), Patrick Morris (UPC) and Katherine Staden (Open U) |
| Organisation | Open University |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint work on project "Universality for transversal Hamilton cycles" initiated at Workshop on spanning subgraphs in graphs and related combinatorial problems at University of Warwick (24-28 July 2023). The topic of the project is related to previous work of the PI on transversal factors and spanning trees in graphs. |
| Collaborator Contribution | Collaborators Candy Bowtell (University of Warwick), Patrick Morris (UPC) and Katherine Staden (Open University) contributed to joint work on project "Universality for transversal Hamilton cycles". All parties involved contributed ideas which jointly led to an interesting result on transversal subgraphs. |
| Impact | We proved an interesting result on adversarial Hamilton cycles in collections of graphs on the same vertex set. The result was written up for publication and the preprint was uploaded to arXiv (https://arxiv.org/abs/2310.04138). The manuscript was submitted for publication to the Journal of the London Mathematical Society. |
| Start Year | 2023 |
| Description | Research collaboration with Candy Bowtell (Warwick), Patrick Morris (UPC) and Katherine Staden (Open U) |
| Organisation | Polytechnic University of Catalonia |
| Country | Spain |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint work on project "Universality for transversal Hamilton cycles" initiated at Workshop on spanning subgraphs in graphs and related combinatorial problems at University of Warwick (24-28 July 2023). The topic of the project is related to previous work of the PI on transversal factors and spanning trees in graphs. |
| Collaborator Contribution | Collaborators Candy Bowtell (University of Warwick), Patrick Morris (UPC) and Katherine Staden (Open University) contributed to joint work on project "Universality for transversal Hamilton cycles". All parties involved contributed ideas which jointly led to an interesting result on transversal subgraphs. |
| Impact | We proved an interesting result on adversarial Hamilton cycles in collections of graphs on the same vertex set. The result was written up for publication and the preprint was uploaded to arXiv (https://arxiv.org/abs/2310.04138). The manuscript was submitted for publication to the Journal of the London Mathematical Society. |
| Start Year | 2023 |
| Description | Research collaboration with Candy Bowtell (Warwick), Patrick Morris (UPC) and Katherine Staden (Open U) |
| Organisation | University of Warwick |
| Department | Warwick Mathematics Institute |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint work on project "Universality for transversal Hamilton cycles" initiated at Workshop on spanning subgraphs in graphs and related combinatorial problems at University of Warwick (24-28 July 2023). The topic of the project is related to previous work of the PI on transversal factors and spanning trees in graphs. |
| Collaborator Contribution | Collaborators Candy Bowtell (University of Warwick), Patrick Morris (UPC) and Katherine Staden (Open University) contributed to joint work on project "Universality for transversal Hamilton cycles". All parties involved contributed ideas which jointly led to an interesting result on transversal subgraphs. |
| Impact | We proved an interesting result on adversarial Hamilton cycles in collections of graphs on the same vertex set. The result was written up for publication and the preprint was uploaded to arXiv (https://arxiv.org/abs/2310.04138). The manuscript was submitted for publication to the Journal of the London Mathematical Society. |
| Start Year | 2023 |
| Description | Research collaboration with Julia Bottcher and Peter Allen (LSE) |
| Organisation | London School of Economics and Political Science (University of London) |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint work on project "Loose Hamilton cycle decompositions of the clique". |
| Collaborator Contribution | Prof Bottcher and Prof Allen contributed to joint work on project "Loose Hamilton cycle decompositions of the clique". The problem was suggested by Prof Bottcher and Prof Allen and relies on the application of tools developed during their previous work on graph packings. |
| Impact | The expected outcome is proof of a conjecture stating that the complete 3-uniform hypergraph can be decomposed into loose Hamilton cycles. This project is in the early stages of development. The project participants are working on developing promising ideas based on reducing the problem to small hypergraph designs. |
| Start Year | 2023 |
| Description | Research collaboration with Kalina Petrova (ETH Zurich) |
| Organisation | ETH Zurich |
| Department | Department of Computer Science |
| Country | Switzerland |
| Sector | Academic/University |
| PI Contribution | PI Y Pehova contributed to joint work on project "Minimum vertex degree conditions for loose spanning trees in 3-graphs". The collaboration was initiated during this visit. |
| Collaborator Contribution | K Petrova contributed to joint work on project "Minimum vertex degree conditions for loose spanning trees in 3-graphs". The collaboration was initiated during this visit. K Petrova also gave a seminar talk at LSE on a different topic from her research portfolio. |
| Impact | Pre-print of a paper titled "Minimum vertex degree conditions for loose spanning trees in 3-graphs" (published on arXiv https://arxiv.org/abs/2301.09630). An extended abstract was submitted and presented at one of the major conferences in the area, EuroComb, in August 2023. The full length paper was submitted to Journal of Combinatorial Theory, Series B. |
| Start Year | 2022 |
| Description | Research collaboration with Katherine Staden (Open University), Emil Powiersky (University of Oxford), Pranshu Gupta (Hamburg) |
| Organisation | Hamburg University of Technology |
| Country | Germany |
| Sector | Academic/University |
| PI Contribution | Joint work on the Erdos-Rotschild problem with forbidden bicoloured triangles |
| Collaborator Contribution | Joint work on the Erdos-Rotschild problem with forbidden bicoloured triangles |
| Impact | Research collaboration on the Erdos-Rotschild problem with forbidden bicoloured triangles. This joint work was started at a workshop Young Researchers in Combinatorics organised by PI Yani Pehova. We completely resolved the generalised Erdos-Rothschild problem for forbidden bicoloured triangles, and developed a general theory of problems of Erdos-Rothschild type for non-monochromatic patterns. A manuscript detailing our findings is in the final stages of preparation. |
| Start Year | 2022 |
| Description | Research collaboration with Katherine Staden (Open University), Emil Powiersky (University of Oxford), Pranshu Gupta (Hamburg) |
| Organisation | Open University |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Joint work on the Erdos-Rotschild problem with forbidden bicoloured triangles |
| Collaborator Contribution | Joint work on the Erdos-Rotschild problem with forbidden bicoloured triangles |
| Impact | Research collaboration on the Erdos-Rotschild problem with forbidden bicoloured triangles. This joint work was started at a workshop Young Researchers in Combinatorics organised by PI Yani Pehova. We completely resolved the generalised Erdos-Rothschild problem for forbidden bicoloured triangles, and developed a general theory of problems of Erdos-Rothschild type for non-monochromatic patterns. A manuscript detailing our findings is in the final stages of preparation. |
| Start Year | 2022 |
| Description | Research collaboration with Katherine Staden (Open University), Emil Powiersky (University of Oxford), Pranshu Gupta (Hamburg) |
| Organisation | University of Oxford |
| Department | Mathematical Institute Oxford |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Joint work on the Erdos-Rotschild problem with forbidden bicoloured triangles |
| Collaborator Contribution | Joint work on the Erdos-Rotschild problem with forbidden bicoloured triangles |
| Impact | Research collaboration on the Erdos-Rotschild problem with forbidden bicoloured triangles. This joint work was started at a workshop Young Researchers in Combinatorics organised by PI Yani Pehova. We completely resolved the generalised Erdos-Rothschild problem for forbidden bicoloured triangles, and developed a general theory of problems of Erdos-Rothschild type for non-monochromatic patterns. A manuscript detailing our findings is in the final stages of preparation. |
| Start Year | 2022 |
| Description | Research collaboration with Matias Pavez-Signe |
| Organisation | University of Warwick |
| Department | Warwick Mathematics Institute |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint research project "Rainbow Hamilton cycles". The collaboration was initiated during the visit. |
| Collaborator Contribution | Dr M Pavez-Signe contributed to joint research project "Rainbow Hamilton cycles". The collaboration was initiated during the visit. Dr Pavez-Signe also gave a research talk at LSE on a different topic from his research portfolio. |
| Impact | We generated ideas for determining the threshold for the existence of rainbow Hamilton cycles in locally bounded colourings of the Erdos-Renyi random graph G(n,p). The collaboration is currently on pause. |
| Start Year | 2022 |
| Description | Research collaboration with Viresh Patel (Queen Mary, University of London), Jozef Skokan, Francesco Di-Braccio, Joanna Lada (LSE) |
| Organisation | London School of Economics and Political Science (University of London) |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint work on project "Hamilton decompositions of tripartite oriented graphs". The project topic was suggested by PI Y Pehova to Dr V Patel (QMUL) during a 2-day research workshop organised by QMUL in November 2022. The topic attracted other participants and a promising collaboration was formed between QMUL and LSE. |
| Collaborator Contribution | Dr Viresh Patel (QMUL), Prof Jozef Skokan (LSE), Francesco Di-Braccio (PhD student, LSE), Joanna Lada (PhD student, LSE) contributed to joint work on project "Hamilton decompositions of tripartite oriented graphs". The previous expertise on this topic of Dr Viresh Patel was central to resolving initial questions on the topic. |
| Impact | We generated promising ideas on existence of complete and partial Hamilton decompositions in tripartite oriented and directed graphs. We resolved initial questions on decompositions in directed graphs and showed the existence of approximate decompositions in the oriented setting. A manuscript detailing our work is in the final stages of preparation. |
| Start Year | 2022 |
| Description | Research collaboration with Viresh Patel (Queen Mary, University of London), Jozef Skokan, Francesco Di-Braccio, Joanna Lada (LSE) |
| Organisation | Queen Mary University of London |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | PI Yani Pehova contributed to joint work on project "Hamilton decompositions of tripartite oriented graphs". The project topic was suggested by PI Y Pehova to Dr V Patel (QMUL) during a 2-day research workshop organised by QMUL in November 2022. The topic attracted other participants and a promising collaboration was formed between QMUL and LSE. |
| Collaborator Contribution | Dr Viresh Patel (QMUL), Prof Jozef Skokan (LSE), Francesco Di-Braccio (PhD student, LSE), Joanna Lada (PhD student, LSE) contributed to joint work on project "Hamilton decompositions of tripartite oriented graphs". The previous expertise on this topic of Dr Viresh Patel was central to resolving initial questions on the topic. |
| Impact | We generated promising ideas on existence of complete and partial Hamilton decompositions in tripartite oriented and directed graphs. We resolved initial questions on decompositions in directed graphs and showed the existence of approximate decompositions in the oriented setting. A manuscript detailing our work is in the final stages of preparation. |
| Start Year | 2022 |
| Description | Research collaboration with Yoshiharu Kohayakawa and Guilherme Mota (University of Sao Paulo) |
| Organisation | Universidade de São Paulo |
| Country | Brazil |
| Sector | Academic/University |
| PI Contribution | PI Y Pehova contributed to joint work on project "Tight spanning trees in 3-uniform hypergraphs". She suggested this as the main topic of study during her 2-month research visit to USP. |
| Collaborator Contribution | Prof Y Kohayakawa and Dr G O Mota (both USP) contributed to joint work on project "Tight spanning trees in 3-uniform hypergraphs". |
| Impact | We resolved a problem on the minimum vertex degree threshold for the existence of bounded degree tight spanning trees in 3-uniform hypergraphs. This result extends PI Yani Pehova's previous work "Embedding loose spanning trees in 3-uniform hypergraphs" (https://arxiv.org/abs/2301.09630). The details of the proof are being finalised and the result will most likely lead to a journal publication. |
| Start Year | 2023 |
| Description | Conference talk at British Early Career Mathematicians' Colloquium, University of Birminhgam, UK |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Postgraduate students |
| Results and Impact | PI Yani Pehova was invited speaker at the British Early Career Mathematicians' Colloquium which took place on 20-21 July 2023 at University of Birmingham, UK. They gave a talk titled "Counting pattern-free colourings of graphs" based on research conducted with the associated award for this entry. The audience included predominantly postgraduate students from pure and applied mathematics. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Contributed talk at European Conference on Combinatorics, Graph Theory and Applications (EuroComb), Prague, Czech Republic |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a contributed talk titled "Minimum vertex degree conditions for loose spanning trees in 3-graphs " at The European Conference on Combinatorics, Graph Theory and Applications (EuroComb) which took place 28 Aug - 1 Sept 2023 in Charles University, Prague, Czech Republic. The talk was based on the outcomes of the associated award (https://arxiv.org/abs/2301.09630) and appeared in the conference proceedings in the form of an extended abstract. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Desert Discrete Math Workshop |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | PI Yani Pehova took part in Desert Discrete Math Workshop which took place on 21-27 Jan 2024 at Steele/Burnand Anza-Borrego Desert Research Center (SBABDRC), Borrego Springs, CA, USA. The workshop was jointly organised by University of California Irvine and University of California San Diego. The PI took part in a research focus group working on hypergraph Turan densities of daisies. |
| Year(s) Of Engagement Activity | 2023 |
| Description | LSE Winter Workshop in Combinatorics |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Week-long research workshop took place in the week of 12-16 Dec 2022. About 25 participants took part in focus groups working on different problems in the field of combinatorics. PI Yani Pehova co-organised the workshop together with colleagues from LSE. The main outcome of the workshop is the foundation of new research collaborations, which are expected to continue as longer-term research projects. |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://personal.lse.ac.uk/boettche/2022workshop/ |
| Description | London Colloquia in Combinatorics |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova co-organised and attended the annual Colloquia in Combinatorics which took place on 10-11 May 2023 at Queen Mary, University of London and The London School of Economics. The PI is co-organising the next edition of the Colloquia which will take place on 8-9 May 2024. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://www.lse.ac.uk/Colloquia-in-Combinatorics |
| Description | Pernambuco Workshop on Extremal Combinatorics |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | The Pernambuco Workshop on Extremal Combinatorics (Workshop Pernambucano de Combinatória Extremal) was a small research-focused event including researchers from Brazil and abroad. There were a small amount of research talks and the participants worked mainly on open problems in the area of extremal combinatorics. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://sites.google.com/view/workshopernambucomb/home?authuser=1 |
| Description | QMUL Workshop in Extremal Combinatorics |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Postgraduate students |
| Results and Impact | On 9 and 11 November 2022 Dr Robert Johnson from Queen Mary, University of London organised a joint workshop in extremal combinatorics with invited participants from QMUL, LSE and UCL. Most participants were research students, the others being faculty and postdocs whose research interests fall within the area. PI Yani Pehova took part in the workshop by proposing a research problem and leading a focus group working on it. The main outcome of the workshop is a new research collaboration on Hamilton cycle decompositions of tripartite directed and oriented graphs, which is likely to lead to a journal publication. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Seminar talk at Brunel University, London, UK |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a talk titled "Extremal questions about graphs" at Mathematics and Statistics Research Seminar on 19 Oct 2022 at Brunel University, London, UK. The talk was attended by a general audience of mathematics researchers. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Seminar talk at IMPA, Rio de Janeiro, Brazil |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a talk titled "Transversal factors and spanning trees" at Probability and Combinatorics Seminar on 24 Mar 2023 at IMPA, Rio de Janeiro, Brazil. This was a research seminar talk intended to disseminate outcomes of previous work of the PI to interested researchers at IMPA. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Seminar talk at LSE, London, UK |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a talk titled "Transversal factors and spanning trees" at Combinatorics, Games and Optimisation seminar on 17 Nov 2022 at the London School of Economics. This was a research seminar talk intended to disseminate outcomes of previous work to interested researchers at LSE. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Seminar talk at Universidade de São Paulo, Brazil |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a talk titled "Transversal factors and spanning trees" at Seminários em Combinatória Extremal, Probabilística e Aditiv on 31 Mar 2023 at Universidade de São Paulo, Brazil. This was a research seminar talk disseminating the PI's research to an audience of postgraduate students and faculty members. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Seminar talk at University College London |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a seminar talk titled "Universality for transversal Hamilton cycles" at the Combinatorics Seminar at University College London on 13 Nov 2023. This was a seminar talk disseminating the outcomes of the associated award to an audience of interested researchers at UCL. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Seminar talk at University of Cardiff, UK |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a talk titled "Spanning trees in hypergraphs" at Discrete Mathematics & Data Science Seminar on 24 Jan 2023 at the University of Cardiff, UK. The talk was attended by researchers slightly outside the topic of the talk. A major outcome of the talk was popularising extremal combinatorics among researchers working in other fields of mathematics. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Seminar talk at University of Victoria, Canada |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a research talk titled "The Erdos-Rothschild problem for dichromatic triangles" at Discrete Mathematics Seminar on 18 Jan 2024 at University of Victoria, Canada. This was a research seminar talk disseminating outcomes of the associated award to interested researchers at University of Victoria. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Seminar talk at University of Warwick |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova gave a talk titled "The Erdos-Rothschild problem for dichromatic triangles" at the Combinatorics Seminar at University of Warwick on 27 Oct 2023. This was a research seminar talk intended to disseminate the research outcomes of the associated award to interested researchers at University of Warwick. |
| Year(s) Of Engagement Activity | 2023 |
| Description | UCL Workshop in Extremal and Probabilistic Combinatorics |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova took part in the UCL Workshop in Extremal and Probabilistic Combinatorics which took place at University College London on 2-5 May 2023. The PI was part of a working group considering antipodal paths with few colour changes in colourigns of the hypercube. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Workshop Chileno-Paulista em/en Grafos |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | The fourth edition of the joint Workshop Chileno-Paulista em/en Grafos gathered researchers mainly from Chile and São Paulo that have been working in Combinatorics and Graph Theory. PI Yani Pehova attended the workshop during her 2-month visit to University of São Paulo, together with her collaborators. The workshop has no invited talks and is mainly focused on collaborative work on open problems from the area of extremal and structural combinatorics. |
| Year(s) Of Engagement Activity | 2023 |
| URL | http://professor.ufabc.edu.br/~carla.negri/chipagra/2023/ |
| Description | Workshop in spanning subgraphs in graphs and related combinatorial problems, University of Warwick, UK |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Other audiences |
| Results and Impact | PI Yani Pehova attended Workshop in spanning subgraphs in graphs and related combinatorial problems which took place on 24-28 July 2023 at University of Warwick, UK. The PI took part in a research focus group working on transversal problems in Dirac graphs. The output of the collaboration has been uploaded to arXiv and submitted to a journal (https://arxiv.org/abs/2310.04138). |
| Year(s) Of Engagement Activity | 2023 |