Fibres and ordered set coloring

Dwight Duffus, Henry Kierstead, W. T. Trotter

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

A fibre F of a partially ordered set P is a subset which intersects each nontrivial maximal antichain of P. Let λ be the smallest constant such that each finite partially ordered set P contains a fibre of size at most λ |P|. We show that λ \ ̌ 2 3 by finding a good 3-coloring of the nontrivial antichains of P. Some decision problems involving fibres are also considered. For instance, it is shown that the problem of deciding if a partially ordered set has a fibre of size at most κ is NP-hard.

Original languageEnglish (US)
Pages (from-to)158-164
Number of pages7
JournalJournal of Combinatorial Theory, Series A
Volume58
Issue number1
DOIs
StatePublished - Sep 1991

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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