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.
|Title of host publication||Combinatorial Mathematics|
|Subtitle of host publication||Proceedings of the International Conference on Combinatorial Theory Canberra, August 16-27, 1977|
|Editors||D A Holton, Jennifer Seberry|
|Place of Publication||Berlin Germany|
|Number of pages||8|
|Publication status||Published - 1978|
|Name||Lecture Notes in Mathematics|