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C k -factorization of complete bipartite graphs

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Abstract

In this paper, it is shown that a necessary and sufficient condition for the existence of aC k-factorization ofK m,n is (i)m = n ≡ 0 (mod 2), (ii)k ≡ 0 (mod 2),k ≥ 4 and (iii) 2n ≡ 0 (modk) with precisely one exception, namely m =n = k = 6.

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References

  1. Horton, J.D., Roy, B.K., Schellenberg, P.J., Stinson D.R.: On decomposing graphs into isomorphic uniform 2-factors, Ann. Discrete Math.27, 297–320 (1985)

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  2. Sotteau, D.. Decomposition ofK m, n (K *m,n ) into cycles (circuits) of length 2k. J. Comb. Theory (B)30, 75–81 (1981)

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Authors and Affiliations

  1. Department of Information Science, Faculty of Science, University of Tokyo, 113, Tokyo, Japan

    Hikoe Enomoto

  2. Support System Development Department, Micro Computer Software Development Laboratory, NEC Corporation, Shibaura, Minato-ku, 108, Tokyo, Japan

    Takashi Miyamoto

  3. Department of Industrial Engineering, Faculty of Science and Technology, Kinki University, 577, Osaka, Japan

    Kazuhiko Ushio

Authors
  1. Hikoe Enomoto
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  2. Takashi Miyamoto
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  3. Kazuhiko Ushio
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Enomoto, H., Miyamoto, T. & Ushio, K. C k -factorization of complete bipartite graphs. Graphs and Combinatorics 4, 111–113 (1988). https://doi.org/10.1007/BF01864159

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  • DOI: https://doi.org/10.1007/BF01864159

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