6长圈加1条弦的图设计

Decompositions of K_v into C_6^(r)

设λK_v是λ重v点完全图,G是无孤立点的有限简单图.将G-设计记作(v,G,λ)-GD,是指一个序偶(X,),其中X是完全图K_v的顶点集,是K_v中同构于G的子图(区组)的集合,使得K_v中每条边恰好出现在的λ个区组中.解决了图6长圈加1条弦的图设计问题,并给出其λ=1时的存在谱.

Let rKv be the complete multigraph with v vertices, G be a finite simple graph. A G-decom-position of rK,v denoted by ( v, G, r )-GD is a pair( X ,SS) , where X is the vertex set of Kv and SB is a collection of subgraphs of Kv, such that each subgraph is isomorphic to G and any edge in Kv appear in exact A subgraphs of 96. The discussed graphs are C6(r) ,and the existence of ( v, C6(r) ,1)-GD has been completely solved.