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Tight bounds on maximal and maximum matchings

By Therese Biedl, Erik D. Demaine, Christian A. Duncan, Rudolf Fleischer and Stephen G. Kobourov


Abstract. In this paper, we study bounds on maximal and maximum matchings in special graph classes, specifically triangulated graphs and graphs with bounded maximum degree. For each class, we give a lower bound on the size of matchings, and prove that it is tight for some graph within the class. 1 Introduction The problem of finding a maximum matching in a graph has a long and dis-tinguished history beginning with the early work of Petersen [10], K"onig [8], Hall [5], and Tutte [12]. The fastest algorithms to find a maximum matching inan n-vertex m-edge graph takes O(pnm) time, for bipartite graphs [6] as wellas for general graphs [9]

Year: 2004
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