On component factors

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.

[1]  David P. Sumner,et al.  Graphs with 1-factors , 1974 .

[2]  G. Chartrand,et al.  Graphs & Digraphs , 1986 .