The Intersection Problem for Maximum Pentagon Packings

Let \(K_n\) be the complete graph on \(n\) vertices. Let \(I(X)\) denote the set of integers \(k\) for which a pair of maximum pentagon packings of graph \(X\) exist having \(k\) common 5-cycles. Let \(J(n)\) denote the set \(\{0,1,2,\ldots,P-2,P\}\), where \(P\) is the number of 5-cycles in a maximum pentagon packing of \(K_n\). This paper shows that \(I(K_n) = J(n)\), for all \(n \geq 1\).