Steiner pentagon covering designs Original Research Article

Let Kn denote the complete undirected graph on n vertices. A Steiner pentagon covering design (SPCD) of order n is a pair (Kn,B), where B is a collection of c(n)=⌈n/5⌈n−1/2⌉⌉ pentagons from Kn 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.