Allen, Peter, Böttcher, Julia, Griffiths, Simon, Kohayakawa, Yoshiharu and Morris, Robert
(2017)
Chromatic thresholds in sparse random graphs.
Random Structures & Algorithms, 51 (2).
pp. 215236.
ISSN 10429832
Abstract
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 Hfree 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: 
http://onlinelibrary.wiley.com/journal/10.1002/(IS... 
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: 
2010/095557, 2009/178317, 500016/20102, 308509/20072, 479032/20122, 303275/20138, 484154/20109, EP/J019496/1 
Funders: 
São Paulo Research Foundation, National Council for Scientific and Technological Development, Engineering and Physical Sciences Research Council 
URI: 
http://eprints.lse.ac.uk/id/eprint/66978 
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