\(H\)-decompositions of \(r\)-graphs when \(H\) is an \(r\)-graph with exactly 2 edges (Q2380474)

Summary: Given two \(r\)-graphs \(G\) and \(H\), an \(H\)-decomposition of \(G\) is a partition of the edge set of \(G\) such that each part is either a single edge or forms a graph isomorphic to \(H\). The minimum number of parts in an \(H\)-decomposition of \(G\) is denoted by \(\phi^r_H(G)\). By a 2-edge-decomposition of an \(r\)-graph we mean an \(H\)-decomposition for any fixed \(r\)-graph \(H\) with exactly 2 edges. In the special case where the two edges of \(H\) intersect in exactly \(1\), \(2\) or \(r-1\) vertices these 2-edge-decompositions will be called bowtie, domino and kite respectively. The value of the function \(\phi^r_H(n)\) will be obtained for bowtie, domino and kite decompositons of \(r\)-graphs.