The solution and applications of a combinatorial problem

被引：0

作者：

Xu, Gaokui ^{[1
,2
]}

Li, Shengjia ^{[1
]}

Guo, Qiaoping ^{[2
]}

Li, Hongwei ^{[2
]}

机构：

[1] Shanxi Univ, Inst Math & Appl Math, Taiyuan 030006, Shanxi, Peoples R China

[2] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

DISCRETE APPLIED MATHEMATICS | 2012年 / 160卷 / 10-11期

基金：

中国国家自然科学基金;

关键词：

Integer; Set; Map;

D O I：

10.1016/j.dam.2012.02.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we solve the following combinatorial problem. Let A(1), A(2), ... ,A(p) be given sets and B-1, B-2, ... ,B-q be m-sets. We lower bound the number q of sets B-1, B-2, ... ,Bq such that boolean OR(p)(i=1) A(i) subset of boolean OR(q)(i=1) B-i, and, for each i is an element of {1, 2, ... , q}, the set B-i does not contain two distinct elements x and y with x is an element of A(j), y is an element of A(k) and j not equal k. Our result directly implies the theorems proved by Bessy et al. [S. Bessy, N. Lichiardopol, J.-S. Sereni, Two proofs of the Bermond-Thomassen conjecture for tournaments with bounded minimum in-degree, Discrete Math. 310 (C) (2010) 557-560]. 2012 Elsevier B.V. All rights reserved.

引用

页码：1643 / 1649

页数：7

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