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The chromatic threshold of graphs

Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Griffiths, Simon and Kohayakawa, Yoshiharu (2013) The chromatic threshold of graphs. Advances in Mathematics, 235. pp. 261-295. ISSN 0001-8708

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Identification Number: 10.1016/j.aim.2012.11.016


The chromatic threshold δχ(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 χ(G)⩽C. We prove that for every graph H with χ(H)=r⩾3. We moreover characterise the graphs H with a given chromatic threshold, and thus determine δχ(H) for every graph H. This answers a question of Erdős and Simonovits [P. Erdős, M. Simonovits, On a valence problem in extremal graph theory, Discrete Math. 5 (1973), 323–334], and confirms a conjecture of Łuczak and Thomassé [Tomasz Łuczak, Stéphan Thomassé, Colouring dense graphs via VC-dimension, arXiv:1011.4310 (submitted for publication)].

Item Type: Article
Official URL:
Additional Information: © 2013 Elsevier Ltd.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 28 Jan 2013 09:22
Last Modified: 25 Jun 2024 21:48

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