A lower bound on the acyclic matching number of subcubic graphs

The acyclic matching number of a graph G is the largest size of an acyclic matching in G, that is, a matching M in G such that the subgraph of G induced by the vertices incident to edges in M is a forest. We show that the acyclic matching number of a connected subcubic graph G with m edges is at least m∕6 except for two graphs of order 5 and 6.