Two sufficient conditions for component factors in graphs

Abstract

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) 2 2k+1 ; (ii) a graph G with (G) 2 is a {K 1,1 , K 1,2 , . . . , K 1,k , T (2k + 1)}-factor deleted graph if its binding number bind(G) 2 2k-1 .

Topics & Concepts