Maximal Induced Matchings in Triangle-Free Graphs
نویسندگان
چکیده
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 ≈ 1.5849 maximal induced matchings, and this bound is best possible. We prove that every n-vertex triangle-free graph has at most 3 ≈ 1.4423 maximal induced matchings, and 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 O(1.4423), yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.
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