Packing the Crowns with Cycles and Stars

Let \( F, G \) and \( H \) be graphs. A \( (G, H) \)-decomposition of \( F \) is a partition of the edge set of \( F \) into copies of \( G \) and copies of \( H \) with at least one copy of \( G \) and at least one copy of \( H \). For \( L \subseteq F \), a \( (G, H) \)-packing of \( F \) with leave \( L \) is a \( (G, H) \)-decomposition of \( F – E(L) \). A \( (G, H) \)-packing of \( F \) with the largest cardinality is a maximum \( (G, H) \)-packing. This paper gives the solution of finding the maximum \( (C_k, S_k) \)-packing of the crown \( C_{n, n-1} \).