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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 $Δ$, and no isolated vertex, has an acyclic matching of size at least (1-o(1))6n/Δ², and we explain how to find such an acyclic matching in polynomial time.
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Baste et al. (2020) studied this question.
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