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On component factors

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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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References

  1. Behzad, M., Chartrand, G., Lesniak-Foster, L.: Graphs & Digraphs. Boston: Prindle, Weber & Schmidt, 1979

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  2. 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

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