Basavaraju, M.Heggernes, P.van 't'Hof, P.Saei, R.Villanger, Y.2026-02-052016Journal of Graph Theory, 2016, 83, 3, pp. 231-2503649024https://doi.org/10.1002/jgt.21994https://idr.nitk.ac.in/handle/123456789/25890An 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.Combinatorial boundsExtremal graphInduced matchingsPolynomial delaysTriangle-free graphsGraph theory