Maximal Induced Matchings in Triangle-Free Graphs

Abstract

An induced matching in a graph is a set of edges whose endpoints induce a 1-regular subgraph. It is known that every n-vertex graph has at most (Formula presented.) maximal induced matchings, and this bound is the best possible. We prove that every n-vertex triangle-free graph has at most (Formula presented.) maximal induced matchings; this bound is attained by every disjoint union of copies of the complete bipartite graph K<inf>3, 3</inf>. Our result implies that all maximal induced matchings in an n-vertex triangle-free graph can be listed in time (Formula presented.), yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph. © 2015 Wiley Periodicals, Inc.