A semidefinite programming approach to a cross-intersection problem with measures

Sho Suda, Hajime Tanaka, Norihide Tokushige

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We present a semidefinite programming approach to bound the measures of cross-independent pairs in a bipartite graph. This can be viewed as a far-reaching extension of Hoffman’s ratio bound on the independence number of a graph. As an application, we solve a problem on the maximum measures of cross-intersecting families of subsets with two different product measures, which is a generalized measure version of the Erdős–Ko–Rado theorem for cross-intersecting families with different uniformities.

Original languageEnglish
Pages (from-to)113-130
Number of pages18
JournalMathematical Programming
Volume166
Issue number1-2
DOIs
Publication statusPublished - 2017 Nov 1

Keywords

  • Cross-intersecting families
  • Intersection theorem
  • Measure
  • Semidefinite programming
  • The Erdős–Ko–Rado theorem

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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