A New Class for Large Sets of Almost Hamilton Cycle Decompositions

作者：Zhao, Hong-tao^*

来源：Acta Mathematicae Applicatae Sinica-English Series, 2017, 33(4): 865-870.

DOI：10.1007/s10255-017-0703-0

• large set
• cycle system
• almost Hamilton cycle decomposition
• symmetric group
• complete automorphism group

A k-cycle system of order v with index lambda, denoted by CS(v, k, lambda), is a collection A of k-cycles (blocks) of K-v such that each edge in K-v appears in exactly lambda blocks of A. A large set of CS(v, k, lambda)s is a partition of the set of all k-cycles of K-v into CS(v, k, lambda)(s), and is denoted by LCS(v, k, lambda). A (v - 1)-cycle in K-v is called almost Hamilton. The completion of the existence problem for LCS(v, v-1, lambda) depends only on one case: all v >= 4 for lambda = 2. In this paper, it is shown that there exists an LCS(v, v - 1, 2) for all v equivalent to 2 (mod 4), v >= 6.

• 出版日期2017-10
• 单位华北电力大学（保定）; 华北电力大学