Abstract
A pentagonal packing PP( n; t) is a family of t edge-disjoint pentagons in the complete graph K n . A pentagonal packing is maximal if the complement of the union of its pentagons is pentagon-free. The spectrum S (5)( n) for maximal pentagonal packings is the set of sizes t such that there exists a maximal PP( n; t). We determine the extremes of the spectrum S (5)( n) for all n. Our results may be viewed as an extension of similar results for maximal partial Steiner triple systems.
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