Maximum Induced Matching of Hexagonal Graphs

Abstract

A matching in a graph is a set of edges no two of which share a common vertex. A matching is an induced matching if no two edges in the matching have a third edge in the graph connecting them. The problem of finding a maximum induced matching or shortly MIM is known to be NP-hard in general, and it remains so even when the input graph is bipartite. The decision problem of MIM is NP-complete in general, and it remains NP-complete even if restricted to several classes of graphs. On the other hand, the problem has been shown to be polynomial for some special sets of graphs. In this paper, we give tight upper and lower bounds on maximum induced matching in special subset of planar graphs, called hexagonal graphs.

Efficient algorithms for maximum induced matching problem in permutation and trapezoid graphs

“…Besides, it is known for polynomial-time maximum induced matching on special graph classes such as co-comparability graphs (including circular-arc graphs [10], interval graphs [11], etc. ), circular-convex bipartite and triad-convex bipartite graphs [12], AT-free graphs [13] and hexagonal graphs [14]. In chordal graphs, finding a MIM can be done in linear time [15].…”