Library Header Image
LSE Research Online LSE Library Services

The chromatic threshold of graphs

Allen, Peter, Böttcher, Julia, Griffiths, Simon and Kohayakawa, Yoshiharu (2013) The chromatic threshold of graphs. Advances in Mathematics, 235. pp. 261-295. ISSN 0001-8708

Full text not available from this repository.

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
Sets: Departments > Mathematics
Date Deposited: 28 Jan 2013 09:22
Last Modified: 20 Nov 2019 10:48

Actions (login required)

View Item View Item