Brightwell, Graham, Panagiotou, Konstantinos and Steger, Angelika (2012) Extremal subgraphs of random graphs. Random structures & algorithms, 41 (2). pp. 147-178. ISSN 1042-9832
Abstract
We prove that there is a constant c > 0, such that whenever p ≥ n -c, with probability tending to 1 when n goes to infinity, every maximum triangle-free subgraph of the random graph G n,p is bipartite. This answers a question of Babai, Simonovits and Spencer (Babai et al., J Graph Theory 14 (1990) 599-622). The proof is based on a tool of independent interest: we show, for instance, that the maximum cut of almost all graphs with M edges, where M ≫ n and M ≤ (n 2)/2, is "nearly unique". More precisely, given a maximum cut C of G n,M, we can obtain all maximum cuts by moving at most O(√n 3/M) vertices between the parts of C.
| Item Type: | Article |
|---|---|
| Official URL: | http://onlinelibrary.wiley.com/journal/10.1002/(IS... |
| Additional Information: | © 2012 Wiley |
| Uncontrolled Keywords: | extremal graph theory, random graphs |
| Library of Congress subject classification: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/43043/ |
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