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

## Abstract

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 |
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Official URL: | http://www.journals.elsevier.com/advances-in-mathe... |

Additional Information: | © 2013 Elsevier Ltd. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 28 Jan 2013 09:22 |

Last Modified: | 20 Oct 2021 03:16 |

URI: | http://eprints.lse.ac.uk/id/eprint/47847 |

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