Maximal Induced Matchings in Triangle-Free Graphs

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 10(n/5) approximate to 1.5849(n) maximal induced matchings, and this bound is the best possible. We prove that every n-vertex triangle-free graph has at most 3(n/3) approximate to 1.4423(n) maximal induced matchings; this bound is attained by every disjoint union of copies of the complete bipartite graph K-3,K-3. Our result implies that all maximal induced matchings in an n-vertex triangle-free graph can be listed in time O(1.4423(n)), yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph. (C) 2015 Wiley Periodicals, Inc.