5 research outputs found
Maximal induced matchings in triangle-free graphs
An induced matching in a graph is a set of edges whose endpoints induce a
-regular subgraph. It is known that any -vertex graph has at most
maximal induced matchings, and this bound is best
possible. We prove that any -vertex triangle-free graph has at most maximal induced matchings, and this bound is attained by any
disjoint union of copies of the complete bipartite graph . Our result
implies that all maximal induced matchings in an -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.Comment: 17 page