Minimum Resolvable Coverings of K-nu with Copies of K-4-e

作者：Su, Renwang^*; Wang, Lidong

来源：Graphs and Combinatorics, 2011, 27(6): 883-896.

DOI：10.1007/s00373-010-1003-0

• Minimum
• Resolvable
• (K-4-e)-coverings
• (K-4-e)-packings

Suppose K-v is the complete undirected graph with v vertices and K-4 - e is the graph obtained from a complete graph K-4 by removing one edge. Let (K-4 - e)MRC(v) denote a resolvable covering of K-v with copies of K-4 - e with the minimum possible number n(v, K-4 - e) of parallel classes. It is readily verified that n(v, K-4 - e) >= inverted right perpendicular2(v - 1)/5inverted left perpendicular. In this article, it is proved that there exists a (K-4 - e)MRC(v) with inverted right perpendicular2(v - 1)/5inverted left perpendicular parallel classes if and only if v equivalent to 0 (mod 4) with the possible exceptions of v = 108, 172, 228, 292, 296, 308, 412. In addition, the known results on the existence of maximum resolvable (K-4 - e)-packings are also improved.

• 出版日期2011-11
• 单位浙江工商大学; 中国人民武装警察部队学院