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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References
Bäbler F.: Über die zerlegung regulärer streckenkomplexe ungerader ordnung. Comment. Math. Helvetici 10, 275–287 (1938)
Hall P.: On representatives of subsets. J. Lond. Math. Soc. 10, 26–30 (1935)
Lovász, L., Plummer, M.D.: Matching Theory. In: Annals of Discrete Mathematics, vol. 29. North-Holland, Amsterdam (1986)
Tutte W.T.: The factorization of linear graphs. J. Lond. Math. Soc. 22, 107–111 (1947)
Tutte W.T.: The factors of graphs. Can. J. Math. 4, 314–328 (1952)
Tutte W.T.: The 1-factors of oriented graphs. Proc. Am. Math. Soc. 4, 922–931 (1953)
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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