An O(n) Time Algorithm For Maximum Induced Matching In Bipartite Star_123-free Graphs

A matching in a graph is a set of edges no two of which share a common vertex. A matching M is an induced matching if no edge connects two edges of M. The problem of finding a maximum induced matching is known to be NP-hard in general and specifically for bipartite graphs. Lozin has been proposed an O(n) time algorithm for this problem on the class of bipartite Star123, Sun4-free graphs. In this paper we improve and generalize this result in presenting a simple O(n) time algorithm for maximum induced matching problem in bipartite Star123-free graphs. Keywords-Bipartite graph; Decomposition of graphs; Design and analysis of algorithms; Matching; Induced Matching.