(1) Department of Applied Mathematics, Science University of Tokyo, Kagurazaka Shinjuku-ku, 162 Tokyo, Japan;(2) Department of Information Science, Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, 113 Tokyo, Japan
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.