Solving the Maximum Matching Problem on Bipartite <i>Star</i><sub>123</sub>-Free Graphs in Linear Time

Abstract

The bipartite Star123-free graphs were introduced by V. Lozin in [1] to generalize some already known classes of bipartite graphs. In this paper, we extend to bipartite Star123-free graphs a linear time algorithm of J. L. Fouquet, V. Giakoumakis and J. M. Vanherpe for finding a maximum matching in bipartite Star123, P7-free graphs presented in [2]. Our algorithm is a solution of Lozin's conjecture.