O(n) time algorithms for dominating induced matching problems

Abstract

We describe O(n) time algorithms for finding the minimum weighted dominating induced matching of chordal, dually chordal, biconvex, and claw-free graphs. For the first three classes, we prove tight O(n) bounds on the maximum number of edges that a graph having a dominating induced matching may contain. By applying these bounds, countings and employing existing O(n+m) time algorithms we show that they can be reduced to O(n) time. For claw-free graphs, we describe an algorithm based on that by Cardoso, Korpelainen and Lozin [4], for solving the unweighted version of the problem, which decreases its complexity from O(n 2) to O(n), while additionally solving the weighted version. © 2014 Springer-Verlag Berlin Heidelberg.