Maximal Induced Matchings in Triangle-Free Graphs
Manu Basavaraju, Pinar Heggernes, Pim van ’t Hof, Reza Saei, Yngve Villanger · Journal of Graph Theory · 2015
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 maximal induced matchings, and this bound is the best possible. We prove that every n-vertex triangle-free graph has at most maximal induced matchings; this bound is attained by every disjoint union of copies of the complete bipartite graph K3, 3. Our result implies that all maximal induced matchings in an n-vertex triangle-free graph can be listed in time , yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.