6 citations · 34 across the 27 of their papers we have counts for
5 papers · 1 filter
The -Ramsey problem for triangle-free graphs
Ewan Davies, Freddie Illingworth
In 1967, Erdős asked for the greatest chromatic number, , amongst all -vertex, triangle-free graphs. An observation of Erdős and Hajnal together with Shearer's classical u…
A note on induced Turán numbers
Freddie Illingworth
Loh, Tait, Timmons and Zhou introduced the notion of induced Turán numbers, defining to be the greatest number of edges in an -vertex…
Product structure of graphs with an excluded minor
Freddie Illingworth, Alex Scott, David R. Wood
This paper shows that -minor-free (and -minor-free) graphs are subgraphs of products of a tree-like graph (of bounded treewidth) and a complete graph .…
Minimum degree stability of -free graphs
Freddie Illingworth
Given an -chromatic graph , the fundamental edge stability result of Erdős and Simonovits says that all -vertex -free graphs have at most $(1 - 1/r + o(1)) \binom…
The chromatic profile of locally colourable graphs
Freddie Illingworth
The classical Andrásfai-Erdős-Sós theorem considers the chromatic number of -free graphs with large minimum degree, and in the case says that any -vertex tria…