Extremal subgraphs of random graphs

Brightwell, Graham, Panagiotou, Konstantinos and Steger, Angelika (2012) Extremal subgraphs of random graphs. Random Structures & Algorithms, 41 (2). pp. 147-178. ISSN 1042-9832

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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
Divisions:	Mathematics
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics
Date Deposited:	16 Apr 2012 11:26
Last Modified:	06 Jan 2024 02:03
URI:	http://eprints.lse.ac.uk/id/eprint/43043

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