Search Results for author: Freddie Illingworth

Found 2 papers, 0 papers with code

Minimum degree stability of $H$-free graphs

no code implementations22 Feb 2021 Freddie Illingworth

Given an $(r + 1)$-chromatic graph $H$, the fundamental edge stability result of Erd\H{o}s and Simonovits says that all $n$-vertex $H$-free graphs have at most $(1 - 1/r + o(1)) \binom{n}{2}$ edges, and any $H$-free graph with that many edges can be made $r$-partite by deleting $o(n^{2})$ edges.

Combinatorics 05C35

The chromatic profile of locally bipartite graphs

no code implementations18 Dec 2020 Freddie Illingworth

Locally bipartite graphs, first mentioned by Luczak and Thomass\'{e}, are the natural variant of triangle-free graphs in which each neighbourhood is bipartite.

Combinatorics 05C15, 05C35

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