A characterization of the subcubic graphs achieving equality in the Haxell‐Scott lower bound for the matching number

In 2004, Biedl et al proved that if G is a connected cubic graph of order n , then α′(G)≥19(4n−1) , where α′(G) is the matching number of G . The graphs achieving equality in this bound were characterized in 2010 by O and West. In 2017, Haxell and Scott proved that if G is a connected subcubic graph, then α′(G)≥49n3(G)+39n2(G)+29n1(G)−19 , where ni(G) denotes the number of vertices of degree i in G . In this paper, we characterize the graphs achieving equality in the lower bound on the matching number given by Haxell and Scott.