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On extremal subgraphs of random graphs

Brightwell, Graham and Panagiotou, Konstantinos and Steger, Angelika (2007) On extremal subgraphs of random graphs. In: 18th ACM-SIAM Symposium on Discrete Algorithms, 7 - 9 January 2007, New Orleans LA, USA.

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Let K-l denote the complete graph on vertices. We prove that there is a constant c = c(l) > 0, such that whenever p >= n(-c), with probability tending to 1 when n goes to infinity, every maximum K-l-free subgraph of the binomial random graph G(n,p) is (l-1)-partite. This answers a question of Babai, Simonovits and Spencer [3]. 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, 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 (root n(3/)M) vertices between the parts of C.

Item Type: Conference or Workshop Item (Paper)
Official URL:
Additional Information: © 2007 The Author
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 21 Oct 2010 13:40
Last Modified: 01 Feb 2018 12:23

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