8长圈加1条弦的图设计

Decompositions of λK_v into C_8^((r))

设λKv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=(X ,B) ,其中X是完全图Kv 的顶点集 ,B是Kv 中同构于G的子图 (区组 )的集合 ,使得Kv 中每条边恰好出现在B的λ个区组中 .利用差分法、拟群及组合设计理论中经典的PBD方法等 ,建立了若干有效的构造图设计的递归方法 ,并给出了若干小设计的直接构造 .最终解决了λ=1时 ,8长圈加 1条弦的图设计的存在性问题 ,并给出其λ

Let λK v be the complete multigraph with v vertices, G be a finite simple graph.A G decomposition of λK v ,denoted by ( v,G,λ ) GD is a pair ( X ,B),where X is the vertex set of K v and B is a collection of subgraphs of K v ,such that each subgraph is isomorphic to G and any edge in K v appear in exact λ subgraphs of B.By difference,quasi group and the dassical PBD method of combinatorial design theory,many effective recursive methods of graph design have been formed and some direct constructure of small number design are given.Eventually,the existence of ( v,C (r) 8,1 ) GD has been completely solved and the existence spectrum is given.