A note on degree sum conditions for 2-factors with a prescribed number of cycles in bipartite graphs |
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Authors: | Shuya Chiba Tomoki Yamashita |
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Institution: | 1. Applied Mathematics, Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan;2. Department of Mathematics, Kindai University, 3-4-1 Kowakae, Higashi-Osaka, Osaka 577-8502, Japan |
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Abstract: | Let be a balanced bipartite graph of order , and let be the minimum degree sum of two non-adjacent vertices in different partite sets of . In 1963, Moon and Moser proved that if , then is hamiltonian. In this note, we show that if is a positive integer, then the Moon–Moser condition also implies the existence of a 2-factor with exactly cycles for sufficiently large graphs. In order to prove this, we also give a condition for the existence of vertex-disjoint alternating cycles with respect to a chosen perfect matching in . |
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Keywords: | 2-factors Degree conditions Bipartite graphs Perfect matchings Alternating cycles |
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