带2条弦的6长圈的图设计

Graph Design for a 6-circuits with Two Chords

λKv是λ重v点完全图,对于有限简单图G,图设计GGDλ(v)是1个序偶(X,B),其中X是Kv的顶点集,区组集B为λKv的全部边的一种分拆,其每个成员(区组)都是与G同构的子图.利用"差方法"、"带洞图设计"等工具,结合一系列小设计的构作,对6点8边图C的图设计进行了讨论,并证明了存在CGD(v) v≡0,1(mod16),v≥6.

Let λK_v be multiple graph with v vertices,and G be a finite simple graph.Graph design G-GD_λ(v) is a pair of (X,B),where X is the vertex set of K_v,and B is a partition of all the edges in λK_v,such that each number of B is isomorphic to G.By means of 'diference method' and 'holey graph design',graph design for a graph C with six vertices and eight edges is discussed,and the following existence result is obtained:C-GD(v) exists if and only if v≡0,1(mod 16),v≥6.