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

Abstract

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.