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Isomorphic factorisations III: Complete multipartite graphs

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Part of the Lecture Notes in Mathematics book series (LNM,volume 686)

Abstract

In the first paper of this series we showed that a factorisation of the complete graph Kp into t isomorphic subgraphs exists whenever the Divisibility Condition holds, that is, the number of lines is divisible by t. Our present objective is to investigate for complete multipartite graphs the extent to which the Divisibility Condition implies the existence of an isomorphic factorisation. We find that this is indeed the situation for all complete bipartite graphs but not for all k-partite graphs when k ≥ 3.

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References

  1. F. Harary, Graph Theory. Addison-Wesley, Reading, Mass., 1969.

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  2. F. Harary, R.W. Robinson and N.C. Wormald, Isomorphic Factorisations I: Complete graphs, Trans. Amer. Math. Soc., to appear.

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  3. F. Harary and W.D. Wallis, Isomorphic factorisations II: Combinatorial designs, Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing, Utilitas Math. Publ., Winnipeg, to appear.

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  4. S. Yamamoto, H. Ikeda, S. Shige-eda, K. Ushio and N. Hamada, On claw-decomposition of complete graphs and complete bigraphs, Hiroshima Math. J. 5 (1975) 33–42.

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© 1978 Springer-Verlag

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Harary, F., Robinson, R.W., Wormald, N.C. (1978). Isomorphic factorisations III: Complete multipartite graphs. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062515

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  • DOI: https://doi.org/10.1007/BFb0062515

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive