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
The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decompos...The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.展开更多
In this paper,we prove that L(K_(x,y))(λ),theλ-fold line graph of the complete bipartite graph Ka,y,has a C_(6)-decomposition if and only if ry≥6,λxy(c+y-2)=0(mod 12)and(x+y)=0(mod 2),where x,y are nonnegative int...In this paper,we prove that L(K_(x,y))(λ),theλ-fold line graph of the complete bipartite graph Ka,y,has a C_(6)-decomposition if and only if ry≥6,λxy(c+y-2)=0(mod 12)and(x+y)=0(mod 2),where x,y are nonnegative integers and(x,y)≠(2,4)or(2,5).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.
基金Supported by the National Natural Science Foundation of China(Grant No.11161032)
文摘The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.
文摘In this paper,we prove that L(K_(x,y))(λ),theλ-fold line graph of the complete bipartite graph Ka,y,has a C_(6)-decomposition if and only if ry≥6,λxy(c+y-2)=0(mod 12)and(x+y)=0(mod 2),where x,y are nonnegative integers and(x,y)≠(2,4)or(2,5).
