Abstract
A Steiner pentagon system is a pair (Kn, P) where Kn isthe complete undirected graph on n vertices. P is a collection of edge-disjoint pentagons which partition Kn, and such that every part of distinct vertices of Kn is joined by a path of length two in exactly one pentagon of the collection P. The number n is called the order of the system. This paper gives a somplete solution of the existence problem of Steiner pentagon systems. In particular it is shown that the spectrum for Steiner pentagon systems (=the set of all orders for which a Steiner pentagon system exists) is precisely the set of all n ≡ 1 or 5 (mod 10), except 15, for which no such system exists.
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