Acyclic matchings in graphs of bounded maximum degree

A matching M in a graph G is acyclic if the subgraph of G induced by the set of vertices that are incident to an edge in M is a forest. We prove that every graph with n vertices, maximum degree at most delta, and no isolated vertex, has an acyclic matching of size at least (1 - o(1)) 6n/delta(2), and we explain how to find such an acyclic matching in polynomial time. (C) 2022 Elsevier B.V. All rights reserved.