Abstract
LetK be a connected graph. A spanning subgraphF ofG is called aK-factor if every component ofF is isomorphic toK. On the existence ofK-factors we show the following theorem: LetG andK be connected graphs andp be an integer. Suppose|G| = n|K| and 1 <p < n. Also suppose every induced connected subgraph of orderp|K| has aK-factor. ThenG has aK-factor.
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Sumner, D.P.: Graphs with 1-factors. Proc. Amer. Math. Soc.,42, 8–12 (1974)
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Egawa, Y., Enomoto, H. & Saito, A. On component factors. Graphs and Combinatorics 2, 223–225 (1986). https://doi.org/10.1007/BF01788096
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DOI: https://doi.org/10.1007/BF01788096