科研之友
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摘要
For a set of positive integers, a spanning subgraph F of a graph G is called an -factor of G if for all vertices x of G, where deg (F) (x) denotes the degree of x in F. We prove the following theorem on {a, b}-factors of regular graphs. Let r a parts per thousand yen 5 be an odd integer and k be either an even integer such that 2 a parts per thousand currency sign k %26lt; r/2 or an odd integer such that r/3 a parts per thousand currency sign k %26lt; r/2. Then every r-regular graph G has a {k, r-k}-factor. Moreover, for every edge e of G, G has a {k, r-k}-factor containing e and another {k, r-k}-factor avoiding e.
- 出版日期2014-7
