Allen, Peter 
ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Griffiths, Simon, Kohayakawa, Yoshiharu and Morris, Robert
(2017)
Chromatic thresholds in sparse random graphs.
Random Structures and Algorithms, 51 (2).
pp. 215-236.
ISSN 1042-9832
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. |
| Divisions: |
Mathematics |
| Subjects: |
Q Science > QA Mathematics |
| Date Deposited: |
22 Jun 2016 13:43 |
| Last Modified: |
12 Dec 2024 01:21 |
| 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 |
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