传递的二部竞赛图的性质

数学季刊 ›› 2003, Vol. 18 ›› Issue (4): 358-363.

传递的二部竞赛图的性质

1．Department of Applied Mathematics ,Petroleum University ,Dongying 257061,China；2．Department of Information and Compute Sciences ,Guangxi Institute of Thchnology ,Liuzhou 545006,China

收稿日期:2001-10-16 出版日期:2003-12-30 发布日期:2024-04-01
作者简介:TAN Shang-wang（1965－）,male,native of Taian,Shandong,an associate professor of Petroleum University , M．S．D．,engages in graph theory .
基金资助:
SupportedbytheGuangxiNationalScienceFoundation( 0 13 10 0 1)；

The Properties of Transitive Bipartite Tournaments

1．Department of Applied Mathematics ,Petroleum University ,Dongying 257061,China；2．Department of Information and Compute Sciences ,Guangxi Institute of Thchnology ,Liuzhou 545006,China

Received:2001-10-16 Online:2003-12-30 Published:2024-04-01
About author:TAN Shang-wang（1965－）,male,native of Taian,Shandong,an associate professor of Petroleum University , M．S．D．,engages in graph theory .
Supported by:
SupportedbytheGuangxiNationalScienceFoundation( 0 13 10 0 1)；

摘要/Abstract

摘要： Let Γ ,n denote all m × n strongly connected bipartite tournaments and α（ m ,n）the maxi- mal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament．Let t（ m ,n ,k ,l）＝ max｛t（ T _{m ,n} ,k ,l）：T _{m ,n} ∈ Γ ,n ｝,where t（ T _{m ,n} ,k ,l）is the
number of k× l（ k ≥2,l ≥2）transitive bipartite subtournaments contained in T _{m ,n} ∈ Γ ,n ．We ob-
tain a method of graph theory for solving some integral programmings,investigate the upper bounds of α（ m ,n）and obtain t（ m ,n ,k ,l）.

关键词: reverse arc, transitive, bipartite tournament, enumeration

Abstract: Let Γ ,n denote all m × n strongly connected bipartite tournaments and α（ m ,n）the maxi- mal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament．Let t（ m ,n ,k ,l）＝ max｛t（ T _{m ,n} ,k ,l）：T _{m ,n} ∈ Γ ,n ｝,where t（ T _{m ,n} ,k ,l）is the
number of k× l（ k ≥2,l ≥2）transitive bipartite subtournaments contained in T _{m ,n} ∈ Γ ,n ．We ob-
tain a method of graph theory for solving some integral programmings,investigate the upper bounds of α（ m ,n）and obtain t（ m ,n ,k ,l）.

Key words: reverse arc, transitive, bipartite tournament, enumeration

中图分类号:

O157.5

谭尚旺, 张德龙 . 传递的二部竞赛图的性质[J]. 数学季刊, 2003, 18(4): 358-363.

TAN Shang-wang , ZHANG De-long . The Properties of Transitive Bipartite Tournaments [J]. Chinese Quarterly Journal of Mathematics, 2003, 18(4): 358-363.

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