Decomposition of complete graphs into stars
- 1 February 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 10 (1) , 23-30
- https://doi.org/10.1017/s0004972700040582
Abstract
A star is a connected graph in which every vertex but one has valency 1. This paper concerns the question of when complete graphs can be decomposed into stars, all of the same order, which have pairwise disjoint edge-sets. It is shown that the complete graphs on rm and rm + 1 vertices, r > 1, can be decomposed into stars with m edges, if and only if r is even or m is odd.Keywords
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