Maximum matching on random graphs
Disordered Systems and Neural Networks
2007-05-23 v1 Statistical Mechanics
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.
Cite
@article{arxiv.cond-mat/0309348,
title = {Maximum matching on random graphs},
author = {Haijun Zhou and Zhong-can Ou-Yang},
journal= {arXiv preprint arXiv:cond-mat/0309348},
year = {2007}
}
Comments
7 pages with 2 eps figures included. Use EPL style. Submitted to Europhysics Letters