On Perfect k-Matchings |
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| Authors: | Hongliang Lu Wei Wang |
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| Institution: | 1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China
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| Abstract: | In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for the existence of perfect k-matchings. We show that a bipartite graph G contains a perfect k-matching if and only if it contains a perfect matching. Moreover, for regular graphs, we provide a sufficient condition for the existence of perfect k-matching in terms of the edge connectivity. |
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