A k-cycle system of order v with index A, denoted by CS（v, k, λ）, is a collection A of k-cycles （blocks） of Kv such that each edge in Kv appears in exactly λ blocks of A. A large set of CS（v, k, λ）s is a part...A k-cycle system of order v with index A, denoted by CS（v, k, λ）, is a collection A of k-cycles （blocks） of Kv such that each edge in Kv appears in exactly λ blocks of A. A large set of CS（v, k, λ）s is a partition of the set of all k-cycles of Kv into CS（v, k, λ）s, and is denoted by LCS（v, k, λ）. A （v - 1）-cycle in K, is called almost Hamilton. The completion of the existence problem for LCS（v, v- 1,λ） depends only on one case： all v ≥ 4 for λ=2. In this paper, it is shown that there exists an LCS（v,v - 1,2） for all v ≡ 2 （mod 4）, v ≥ 6.展开更多
基金Supported in part by the National Natural Science Foundation of China(No.10901051,11201143)the Fundamental Research Funds for the Central Universities(No.2016MS66)the Co-construction Project of Bejing Municipal Commission of Education
文摘A k-cycle system of order v with index A, denoted by CS（v, k, λ）, is a collection A of k-cycles （blocks） of Kv such that each edge in Kv appears in exactly λ blocks of A. A large set of CS（v, k, λ）s is a partition of the set of all k-cycles of Kv into CS（v, k, λ）s, and is denoted by LCS（v, k, λ）. A （v - 1）-cycle in K, is called almost Hamilton. The completion of the existence problem for LCS（v, v- 1,λ） depends only on one case： all v ≥ 4 for λ=2. In this paper, it is shown that there exists an LCS（v,v - 1,2） for all v ≡ 2 （mod 4）, v ≥ 6.
