Chromatic thresholds in sparse random graphs

Allen, Peter, Böttcher, Julia, Griffiths, Simon, Kohayakawa, Yoshiharu and Morris, Robert (2016) Chromatic thresholds in sparse random graphs. Random Structures & Algorithms . ISSN 1098-2418 (In Press)

PDF - Accepted Version Restricted to Repository staff only Download (395Kb)

• LSE expert's profile

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 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:	http://onlinelibrary.wiley.com/journal/10.1002/(IS...
Additional Information:	© 2016 Wiley Periodicals, Inc.
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Mathematics
Project and Funder Information:	Project ID Funder Name Funder ID 2010/09555-7 São Paulo Research Foundation UNSPECIFIED 2009/17831-7 São Paulo Research Foundation UNSPECIFIED 500016/2010-2 National Council for Scientific and Technological Development UNSPECIFIED 308509/2007-2 National Council for Scientific and Technological Development UNSPECIFIED 479032/2012-2 National Council for Scientific and Technological Development UNSPECIFIED 303275/2013-8 National Council for Scientific and Technological Development UNSPECIFIED 484154/2010-9 National Council for Scientific and Technological Development UNSPECIFIED
Date Deposited:	22 Jun 2016 13:43
URL:	http://eprints.lse.ac.uk/66978/

Actions (login required)

Record administration - authorised staff only