Two sufficient conditions for component factors in graphs
Sizhong Zhou, Qiuxiang Bian, Zhiren Sun · Discussiones Mathematicae Graph Theory · 2021
Let G be a graph.For a set H of connected graphs, a spanning subgraph H of a graph G is called an H-factor of G if each component of H is isomorphic to a member of H.An H-factor is also referred as a component factor.If Ge admits an H-factor for any e ∈ E(G), then we say that G is an H-factor deleted graph.Let k ≥ 2 be an integer.In this article, we verify that (i) a graph G admits a {K 1,1 , K 1,2 , . . ., K 1,k , T (2k + 1)}-factor if and only if its binding number bind(G)