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Decomposition of complete graphs into stars

Published online by Cambridge University Press:  17 April 2009

Pauline Cain
Pauline Cain
Affiliation:
Department of Mathematics, University of Newcaztle, Newcastle, New South Wales.
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 23 - 30
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Ae, Tadashl, Yamamoto, Seigo, Yoshida, Noriyoshi, “Line-disjoint decomposition of complete graph into stars”, J. Combinatorial Theory Ser. B (to appear).Google Scholar