Finding Dominating Induced Matchings in P9-Free Graphs in Polynomial Time

Abstract

Let G = (V, E) be a finite undirected graph. An edge subset E′ ⊆ E is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of E′. The Dominating Induced Matching (DIM) problem asks for the existence of a d.i.m. in G. The DIM problem is 𝕅𝕇-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but was solved in linear time for P7-free graphs and in polynomial time for P8-free graphs. In this paper, we solve it in polynomial time for P9-free graphs.

Keywords

• dominating induced matching
• p9-free graphs
• polynomial time algorithm
• 05c69
• 68r10