On connected [g, f+1]-factors in graphs

摘要

Let G = (V(G),E(G)) be a graph with vertex set V(G) and edge set E(G), and g and f two positive integral functions from V(G) to Z(+) - {1} such that g(v) <= f (v) <= d(G)(v) for all v G V(G), where dG (V) is the degree of the vertex v. It is shown that every graph G, including both a [g, f]-factor and a hamiltonian path, contains a connected [g, f + 1]-factor. This result also extends Kano's conjecture concerning the existence of connected [k, k + 1]-factors in graphs.