Steiner pentagon covering designs

作者：Abel RJR; Bennett FE^*; Zhang H; Zhu L

来源：Discrete Mathematics, 2001, 231(1-3): 11-26.

DOI：10.1016/S0012-365X(00)00302-2

• holey Steiner pentagon system
• covering
• packing

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.

• 出版日期2001-3-28
• 单位苏州大学; 宿州学院