Project description DEENESFRITPL New study aims to resolve problems related to spanning subgraphs Graph theory – the study of mathematical structures used to model pairwise relations between objects – has numerous natural connections to other areas, such as combinatorics and theoretical computer science. A fundamental meta-problem in graph theory is the following: given a graph H, what conditions guarantee that another graph G contains a copy of H as a subgraph? The EU-funded SSiGraph project will address a range of exciting and challenging extremal and probabilistic problems on spanning subgraphs in random and coloured graphs. The specific objectives represent a carefully selected range of related major outstanding problems, whose solution would mark truly significant progress in the field. Show the project objective Hide the project objective Objective Graph Theory is a highly active area of Combinatorics with strong links to fields such as Optimisation and Theoretical Computer Science. A fundamental meta-problem in Graph Theory is the following: given a graph H, what conditions guarantee that another graph G contains a copy of H as a subgraph? This is particularly important when H is spanning, i.e. where G and H have the same number of vertices.This project will address a range of exciting and challenging extremal and probabilistic problems on spanning subgraphs in graphs, in the following two interrelated areas: 1. Spanning subgraphs in random graphs: A key aim of Probabilistic Combinatorics is to determine the density threshold for the appearance of different subgraphs in random graphs. This is particularly difficult when the subgraph is spanning, where the known results and techniques are typically highly specific. This project will lead to a unified paradigm for studying thresholds of spanning subgraphs by introducing and developing a new coupling technique. This will provide an excellent platform to study the Kahn-Kalai conjecture, a bold general conjecture on appearance thresholds, and problems including hitting-time conjectures and universality problems.2. Spanning subgraphs in coloured graphs: Many different combinatorial problems are expressible using edge coloured graphs, including Latin square problems dating back to Euler. My objectives here concern long-standing problems on spanning trees, cycles and matchings, and, through this, the resolution of several famous labelling and packing problems.In preliminary work I have developed techniques to study these problems, techniques which will have a far reaching impact, and certainly lead to further applications, e.g. with hypergraphs and resilience problems. The objectives represent a carefully selected range of related major outstanding problems, whose solution would mark truly significant progress in the field. Fields of science natural sciencescomputer and information sciencescomputational sciencenatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2020-STG - ERC STARTING GRANTS Call for proposal ERC-2020-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Coordinator THE UNIVERSITY OF WARWICK Net EU contribution € 1 226 107,29 Address Kirby corner road - university house CV4 8UW Coventry United Kingdom See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Beneficiaries (2) Sort alphabetically Sort by Net EU contribution Expand all Collapse all THE UNIVERSITY OF WARWICK United Kingdom Net EU contribution € 1 226 107,29 Address Kirby corner road - university house CV4 8UW Coventry See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 THE UNIVERSITY OF BIRMINGHAM Participation ended United Kingdom Net EU contribution € 191 257,71 Address Edgbaston B15 2TT Birmingham See on map Region West Midlands (England) West Midlands Birmingham Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
