11 papers
Disproof of the tree product conjecture via the Heisenberg group
Freddie Illingworth, Sergey Norin, Raphael Steiner
Product structure theory aims to understand complex graphs by embedding them into products of simpler graphs. In this direction, Campbell, Distel, Gollin, Harvey, Hendrey, Hickingb…
Non-Homotopic Drawings of Multigraphs
António Girão, Freddie Illingworth, Alex Scott +1
A multigraph drawn in the plane is non-homotopic if no two edges connecting the same pair of vertices can be continuously deformed into each other without passing through a vertex,…
The Zarankiewicz problem on tripartite graphs
Francesco Di Braccio, Freddie Illingworth
In 1975, Bollobás, ErdÅs, and Szemerédi asked for the smallest such that an tripartite graph with minimum degree must contain ,…
The Dominating 4-Colour Theorem
António Girão, Freddie Illingworth, Bojan Mohar +6
A "dominating -model" in a graph is a sequence of pairwise vertex-disjoint connected subgraphs of , such that whenever every vertex…
Relative Turán densities for ordered graphs: all and nothing
Freddie Illingworth, Arjun Ranganathan, Leo Versteegen +1
Reiher, Rödl, Sales, and Schacht initiated the study of relative Turán densities of ordered graphs and showed that it is more subtle and interesting than the unordered case. For…
Treedepth and 2-treedepth in graphs with no long induced paths
JÄdrzej Hodor, Freddie Illingworth, Tomasz Mazur
Huynh, Joret, Micek, Seweryn, and Wollan (Combinatorica, 2022) introduced a graph parameter, later referred to as 2-treedepth and denoted . The parameter is t…