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A degree condition for a graph to have [a,b]-factors

✍ Scribed by Li, Yanjun; Mao-cheng, Cai

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 131 KB
Volume: 27
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199801)27:1<1::aid-jgt1>3.0.co;2-u

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a graph of order n, and let a and b be integers such that

a+b 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

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