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Chromatic thresholds in sparse random graphs

Allen, Peter, Böttcher, Julia, Griffiths, Simon, Kohayakawa, Yoshiharu and Morris, Robert (2017) Chromatic thresholds in sparse random graphs. Random Structures & Algorithms, 51 (2). pp. 215-236. ISSN 1042-9832

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Identification Number: 10.1002/rsa.20709


The chromatic threshold δχ(H,p) of a graph H with respect to the random graph G(n,p) is the infimum over d>0 such that the following holds with high probability: the family of H-free graphs G⊂G(n,p) with minimum degree δ(G)≥dpn has bounded chromatic number. The study of δχ(H):=δχ(H,1) was initiated in 1973 by Erd\H{o}s and Simonovits. Recently δχ(H) was determined for all graphs H. It is known that δχ(H,p)=δχ(H) for all fixed p∈(0,1), but that typically δχ(H,p)≠δχ(H) if p=o(1). Here we study the problem for sparse random graphs. We determine δχ(H,p) for most functions p=p(n) when H∈{K3,C5}, and also for all graphs H with χ(H)∉{3,4}.

Item Type: Article
Official URL:
Additional Information: © 2016 Wiley Periodicals, Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 22 Jun 2016 13:43
Last Modified: 20 Jul 2021 02:34
Projects: 2010/09555-7, 2009/17831-7, 500016/2010-2, 308509/2007-2, 479032/2012-2, 303275/2013-8, 484154/2010-9, EP/J019496/1
Funders: São Paulo Research Foundation, National Council for Scientific and Technological Development, Engineering and Physical Sciences Research Council

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