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- Type of Document: Article
- DOI: 10.1007/s00373-013-1324-x
- Abstract:
- For a set S of positive integers, a spanning subgraph F of a graph G is called an S-factor of G if degF(x) ∈ S for all vertices x of G, where degF(x) denotes the degree of x in F. We prove the following theorem on {a, b}-factors of regular graphs. Let r ≥ 5 be an odd integer and k be either an even integer such that 2 ≤ k < r/2 or an odd integer such that r/3 ≤ k < 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
- Keywords:
- Factor of a graph ; Factor of regular graph ; {a, b}-factor
- Source: Graphs and Combinatorics ; Vol. 30, issue. 4 , 2014 , pp. 821-826 ; ISSN: 0911-0119
- URL: http://link.springer.com/article/10.1007%2Fs00373-013-1324-x