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Maximum matching on random graphs

Haijun Zhou·Zhong-can Ou-Yang
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Abstract

The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from each other {\em gradually} emerge. An analytical expression for the max-matching size is also obtained, which agrees well with computer simulations. Discussion is made on this {\em continuous} glassy phase transition and the absence of such a glassy phase in the related minimum vertex covering problem.

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Haijun Zhou, Zhong-can Ou-Yang. 2003-09-15. Maximum matching on random graphs. https://arxiv.org/abs/cond-mat/0309348

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