Steiner pentagon covering designs

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. c © 2001 Elsevier Science B.V. All rights reserved.