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Maximal Induced Matchings in Triangle-Free Graphs
(Wiley-Liss Inc. info@wiley.com, 2016) Basavaraju, M.; Heggernes, P.; van 't'Hof, P.; Saei, R.; Villanger, Y.
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 K3, 3. 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.