Factorisation of complete bipartite graphs into two isomorphic subgraphs

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 1979Publisher:Springer Berlin Heidelberg

Authors: Stephen J. Quinn;

doi: 10.1007/bfb0102688

Factorisation of complete bipartite graphs into two isomorphic subgraphs

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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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