Steiner pentagon covering designs

Abstract Let K n denote the complete undirected graph on n vertices. A Steiner pentagon covering design (SPCD) of order n is a pair (K n , B ) , where B is a collection of c ( n )=⌈ n /5⌈ n −1/2⌉⌉ pentagons from K n such that any two vertices are joined by a path of length 1 in at least one pentagon of B , and also by a path of length 2 in at least one pentagon of B . The existence of SPCDs is investigated. The main approach is to use certain types of holey Steiner pentagon systems. For n even, the existence of SPCDs is established with a few possible exceptions. For n odd, new SPCDs are found which improve an earlier known result. In addition, new results are also found for Steiner pentagon packing designs.