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- Title
A characterization of the subcubic graphs achieving equality in the Haxell‐Scott lower bound for the matching number.
- Authors
Henning, Michael A.; Shozi, Zekhaya B.
- 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.
- Subjects
GRAPH connectivity; EQUALITY
- Publication
Journal of Graph Theory, 2021, Vol 96, Issue 4, p455
- ISSN
0364-9024
- Publication type
Article
- DOI
10.1002/jgt.22624