The chromatic thresholds of graphs

Details The chromatic thresholds of graphs The chromatic thresholds of graphs

2011-08-08

arxiv.org/abs/1108.1746v1

Mathematics

Combinatorics

37 pages, 2 figures

Scientific paper

The chromatic threshold delta_chi(H) of a graph H is the infimum of d>0 such that there exists C=C(H,d) for which every H-free graph G with minimum degree at least d|G| satisfies chi(G)2. We moreover characterise the graphs H with a given chromatic threshold, and thus determine delta_chi(H) for every graph H. This answers a question of Erd\H{o}s and Simonovits [Discrete Math. 5 (1973), 323-334], and confirms a conjecture of {\L}uczak and Thomass\'e [preprint (2010), 18pp].

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