TWO SUFFICIENT CONDITIONS FOR COMPONENT FACTORS IN GRAPHS

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 G - e admits an H-factor for any e is an element of 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,K-1, K-1,K-2, ..., K-1,K-k, T(2k + 1)}-factor if and only if its binding number bind(G) >= 2/2k+1; (ii) a graph G with delta(G) >= 2 is a {K-1,K-1, K-1,K-2, ..., K-1,K-k, T(2k + 1)}-factor deleted graph if its binding number bind(G) >= 2/2k-1.