A generalization of Sperner's theorem and an application to graph orientations

被引：5
|
作者：
Qian, Jianguo [1 ]
Engel, Konrad [2 ]
Xu, Wei [1 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
[2] Univ Rostock, Inst Math, D-18051 Rostock, Germany
来源：
DISCRETE APPLIED MATHEMATICS | 2009年 / 157卷 / 09期
基金：
中国国家自然科学基金;
关键词：
Sperner's theorem; Average distance; Graph orientation; Multifamily of subsets;
D O I：
10.1016/j.dam.2007.09.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A generalization of Sperner's theorem is established: For a Multifamily M = {Y(1),..., Y(p)} of subsets of {1,..., n) in which the repetition of subsets is allowed, a sharp lower bound for the number phi(M) of ordered pairs (i, j) satisfying i not equal j and Y(i) subset of Y(j) is determined. As an application, the minimum average distance of orientations of complete bipartite graphs is determined. (C) 2007 Elsevier B.V. All rights reserved.
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页码：2170 / 2176
页数：7
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