A degree condition for a graph to have [a,b]-factors
Yanjun Li, Mao-cheng Cai · Journal of Graph Theory · 1998
Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. We show that G has an [a, b]-factor if δ(G) ≥ a, n ≥ 2a + b + and max {dG(u), dG(v) ≥ for any two nonadjacent vertices u and v in G. This result is best possible, and it is an extension of T. Iida and T. Nishimura's results (T. Iida and T. Nishimura, An Ore-type condition for the existence of k-factors in graphs, Graphs and Combinat. 7 (1991), 353–361; T. Nishimura, A degree condition for the existence of k-factors, J. Graph Theory 16 (1992), 141–151). about the existence of a k-factor. As an immediate consequence, it shows that a conjecture of M. Kano (M. Kano, Some current results and problems on factors of graphs, Proc. 3rd China–USA International Conference on Graph Theory and Its Application, Beijing (1993). about connected [a, b]-factors is incorrect. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 1–6, 1998