On degree sum conditions for 2-factors with a prescribed number of cycles |
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Authors: | Shuya Chiba |
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Institution: | Applied Mathematics, Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan |
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Abstract: | For a vertex subset of a graph , let be the maximum value of the degree sums of the subsets of of size . In this paper, we prove the following result: Let be positive integers, and let be an -connected graph of order . If for every independent set of size in , then has a 2-factor with exactly cycles. This is a common extension of the results obtained by Brandt et al. (1997) and Yamashita (2008), respectively. |
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Keywords: | Hamilton cycles 2-factors Vertex-disjoint cycles Degree sum conditions |
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