This paper addresses the problem of maximizing the expected size of a matching in the case of unreliable vertices and/or edges. The assumption is that upon failure, remaining vertices that have not been matched may be subject to a new assignment. This process may be repeated a given number of times, and the objective is to end with the overall maximum number of matched vertices. The origin of t...

Given a graph G where a label is associated with each edge, we address the problem of looking for a maximum matching of G using the minimum number of different labels, namely the Labeled Maximum Matching Problem. It is a relatively new problem whose application is related to the timetabling problem [15]. We prove it is NP-complete and present four different mathematical formulations. Moreover, ...

– The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree c is larger than 2.7183, groups of max-matching patterns which differ greatly from each other gradually emerge. An analytical expression for the max-matching size is also obtained, which agrees well with computer simulations. Discussion is made on t...

Let mcm(m,n) and mwm(m,n,N) be the complexities of computing a maximum cardinality matching and a maximum weight matching, and let mcmbi,mwmbi be their counterparts for bipartite graphs, where m,n, and N are the edge count, vertex count, and maximum integer edge weight. Kao, Lam, Sung, and Ting [1] gave a general reduction showing mwmbi(m,n,N) = O(N ·mcmbi(m,n)) and Huang and Kavitha [2] recent...