Let n and k（n ≥ k 〉 1） be two non-negative integers.A k-multi-hypertournament on n vertices is a pair（V,A）,where V is a set of vertices with ｜V｜=n,and A is a set of k-tuples of vertices,called arcs,such that f...Let n and k（n ≥ k 〉 1） be two non-negative integers.A k-multi-hypertournament on n vertices is a pair（V,A）,where V is a set of vertices with ｜V｜=n,and A is a set of k-tuples of vertices,called arcs,such that for any k-subset S of V,A contains at least one（at most k!） of the k! k-tuples whose entries belong to S.The necessary and suffcient conditions for a non-decreasing sequence of non-negative integers to be the out-degree sequence（in-degree sequence） of some k-multi-hypertournament are given.展开更多
Given non-negative integers m,n,h and k with m≥ h 〉 1 and n ≥ k 〉 1, an （h, k）-bipartite hypertournament on m ＋ n vertices is a triple （U, V, A）, where U and V are two sets of vertices with ｜U｜ = m and ｜V...Given non-negative integers m,n,h and k with m≥ h 〉 1 and n ≥ k 〉 1, an （h, k）-bipartite hypertournament on m ＋ n vertices is a triple （U, V, A）, where U and V are two sets of vertices with ｜U｜ = m and ｜V｜ = n, and A is a set of （h ＋ k）-tuples of vertices,called arcs, with at most h vertices from U and at most k vertices from V, such that for any h＋k subsets U1 UV1 of UUV, A contains exactly one of the （h＋k）! （h＋k）-tuples whose entries belong to U1 ∪ V1. Necessary and sufficient conditions for a pair of non-decreasing sequences of non-negative integers to be the losing score lists or score lists of some（h, k）-bipartite hypertournament are obtained.展开更多
文摘Let n and k（n ≥ k 〉 1） be two non-negative integers.A k-multi-hypertournament on n vertices is a pair（V,A）,where V is a set of vertices with ｜V｜=n,and A is a set of k-tuples of vertices,called arcs,such that for any k-subset S of V,A contains at least one（at most k!） of the k! k-tuples whose entries belong to S.The necessary and suffcient conditions for a non-decreasing sequence of non-negative integers to be the out-degree sequence（in-degree sequence） of some k-multi-hypertournament are given.
基金Supported by the National Natural Science Foundation of China(10501021)
文摘Given non-negative integers m,n,h and k with m≥ h 〉 1 and n ≥ k 〉 1, an （h, k）-bipartite hypertournament on m ＋ n vertices is a triple （U, V, A）, where U and V are two sets of vertices with ｜U｜ = m and ｜V｜ = n, and A is a set of （h ＋ k）-tuples of vertices,called arcs, with at most h vertices from U and at most k vertices from V, such that for any h＋k subsets U1 UV1 of UUV, A contains exactly one of the （h＋k）! （h＋k）-tuples whose entries belong to U1 ∪ V1. Necessary and sufficient conditions for a pair of non-decreasing sequences of non-negative integers to be the losing score lists or score lists of some（h, k）-bipartite hypertournament are obtained.
