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On Perfect k-Matchings

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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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Correspondence to Hongliang Lu.

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This work was supported by National Natural Science Foundation of China No. 11101329 and 11071191 and the Fundamental Research Funds for the Central Universities.

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Lu, H., Wang, W. On Perfect k-Matchings. Graphs and Combinatorics 30, 229–235 (2014). https://doi.org/10.1007/s00373-012-1259-7

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  • DOI: https://doi.org/10.1007/s00373-012-1259-7

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