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

  • Authors:

  • Jianguo Qian;Konrad Engel;Wei Xu

  • Affiliations:

  • School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, PR China;University of Rostock, Institute of Mathematics, D-18051 Rostock, Germany;School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, PR China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

Quantified Score

Hi-index 0.04

Visualization

Abstract

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 @f(M) of ordered pairs (i,j) satisfying ij and Y"i@?Y"j is determined. As an application, the minimum average distance of orientations of complete bipartite graphs is determined.