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Factorisation of complete bipartite graphs into two isomorphic subgraphs

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Part of the Lecture Notes in Mathematics book series (LNM,volume 748)

Abstract

A construction method is given which generates all factorisations of the complete bipartite graph K m,n into two isomorphic line disjoint subgraphs. Such subgraphs are called self-complementary bipartite subgraphs, by analogy with ordinary self-complementary graphs. It is shown that the factorisation giving rise to a self-complementary bipartite graph is unique up to isomorphism. Based on this fact a method is developed for counting unlabelled self-complementary bipartite graphs.

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© 1979 Springer-Verlag

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Quinn, S.J. (1979). Factorisation of complete bipartite graphs into two isomorphic subgraphs. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102688

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  • DOI: https://doi.org/10.1007/BFb0102688

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09555-2

  • Online ISBN: 978-3-540-34857-3

  • eBook Packages: Springer Book Archive