Cookies?
Library Header Image
LSE Research Online LSE Library Services

Chromatic thresholds in sparse random graphs

Allen, Peter and Böttcher, Julia and Griffiths, Simon and Kohayakawa, Yoshiharu and Morris, Robert (2017) Chromatic thresholds in sparse random graphs. Random Structures & Algorithms, 51 (2). pp. 215-236. ISSN 1098-2418

[img] PDF - Accepted Version
Restricted to Repository staff only

Download (404kB) | Request a copy

Identification Number: 10.1002/rsa.20709

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.
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 22 Jun 2016 13:43
Last Modified: 19 Sep 2017 14:40
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
URI: http://eprints.lse.ac.uk/id/eprint/66978

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics