In this note it is shown that a necessary and sufficient condition for the existence of a P 3 factorization of complete multipartite graph λK n m is (1) m≥3, (2) mn≡0 (mod 3) and (3) λ(m-1)n≡0 ...In this note it is shown that a necessary and sufficient condition for the existence of a P 3 factorization of complete multipartite graph λK n m is (1) m≥3, (2) mn≡0 (mod 3) and (3) λ(m-1)n≡0 (mod 4).展开更多
A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In ...A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD（v, k, 1） for k = 3 and 4, and shows that there exists an OSPBD（v, k, 1） for any v ≥ k.展开更多
In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime numbe...In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.展开更多
Let Km,n be a completebipartite graph with two partite sets having m and n vertices,respectively. A Kp,q-factorization of Km,n is a set ofedge-disjoint Kp,q-factors of Km,n which partition theset of edges of Km,n. Whe...Let Km,n be a completebipartite graph with two partite sets having m and n vertices,respectively. A Kp,q-factorization of Km,n is a set ofedge-disjoint Kp,q-factors of Km,n which partition theset of edges of Km,n. When p=1 and q is a prime number,Wang, in his paper 'On K1,k-factorizations of a completebipartite graph' (Discrete Math, 1994, 126: 359-364),investigated the K1,q-factorization of Km,n and gave asufficient condition for such a factorization to exist. In the paper'K1,k-factorizations of complete bipartite graphs' (DiscreteMath, 2002, 259: 301-306), Du and Wang extended Wang's resultto the case that q is any positive integer. In this paper, we give a sufficient condition for Km,n to have aKp,q-factorization. As a special case, it is shown that theMartin's BAC conjecture is true when p:q=k:(k+1) for any positiveinteger k.展开更多
文摘In this note it is shown that a necessary and sufficient condition for the existence of a P 3 factorization of complete multipartite graph λK n m is (1) m≥3, (2) mn≡0 (mod 3) and (3) λ(m-1)n≡0 (mod 4).
文摘A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD（v, k, 1） for k = 3 and 4, and shows that there exists an OSPBD（v, k, 1） for any v ≥ k.
文摘In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071056).
文摘Let Km,n be a completebipartite graph with two partite sets having m and n vertices,respectively. A Kp,q-factorization of Km,n is a set ofedge-disjoint Kp,q-factors of Km,n which partition theset of edges of Km,n. When p=1 and q is a prime number,Wang, in his paper 'On K1,k-factorizations of a completebipartite graph' (Discrete Math, 1994, 126: 359-364),investigated the K1,q-factorization of Km,n and gave asufficient condition for such a factorization to exist. In the paper'K1,k-factorizations of complete bipartite graphs' (DiscreteMath, 2002, 259: 301-306), Du and Wang extended Wang's resultto the case that q is any positive integer. In this paper, we give a sufficient condition for Km,n to have aKp,q-factorization. As a special case, it is shown that theMartin's BAC conjecture is true when p:q=k:(k+1) for any positiveinteger k.
