完全图分拆为带两条弦的6-长圈

Decomposition of $\lambda K_v$ into $6$-Circuits with Two Chords

中文关键词:  图设计  带洞图设计  恰二可迁群.

英文关键词:graph design  holey graph design  sharply 2-transitive group.

中文摘要:

      本文主要讨论将完全图分拆为带两条弦的6-长圈问题. 我们利用PBD闭集等组合设计的方法给出了图设计存在的递归构造,又利用恰二可迁群有效地构造了所需的带洞图设计,并且给出了指数和图的边数相等时图设计的统一构造方法.从而给出了图设计的存在谱.

英文摘要:

      In this paper, we discuss the $G$-decomposition of $\lambda K_v$ into $6$-circuits with two chords. We construct some holey $G$-designs using sharply 2-transitive group, and present the recursive structure by PBD. We also give a unified method to construct $G$-designs when the index equals the edge number of the discussed graph. Finally, the existence of $G$-$GD_\lambda(v)$ is given.