Abstract
A q-star is a connected graph with q edges and in which every vertex but one has valency 1. This paper concerns the question of which particular complete graphs can be decomposed into q-stars that have pairwise disjoint edge-sets for the values of q, 6 and 10. It is shown that the complete graphs on m vertices can be decomposed into 6-stars if and only if m is greater than or equal to 12 and m ≡ 0,1,4,9 (mod 12). It is also shown that the complete graphs on m vertices can be decomposed into 10-stars if and only if m is greater than or equal to 20 and m ≡ 0,1,5,16 (mod 20).
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Reference
Pauline Cain, Decomposition of complete graphs into stars, Bull. Austral. Math. Soc. 10 (1974) 23–30.
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© 1975 Springer-Verlag
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Hogarth, P.C. (1975). Decomposition of complete graphs into 6-stars and into 10-stars. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069552
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DOI: https://doi.org/10.1007/BFb0069552
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07154-9
Online ISBN: 978-3-540-37482-4
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