Color-bounded hypergraphs, IV: Stable colorings of hypertrees

Csilla Bujtás, Zsolt Tuza

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We consider vertex colorings of hypergraphs in which lower and upper bounds are prescribed for the largest cardinality of a monochromatic subset and/or of a polychromatic subset in each edge. One of the results states that for any integers s ≥ 2 and a ≥ 2 there exists an integer f (s, a) with the following property. If an interval hypergraph admits some coloring such that in each edge Ei at least a prescribed number si ≤ s of colors occur and also each Ei contains a monochromatic subset with a prescribed number ai ≤ a of vertices, then a coloring with these properties exists with at most f (s, a) colors. Further results deal with estimates on the minimum and maximum possible numbers of colors and the time complexity of determining those numbers or testing colorability, for various combinations of the four color bounds prescribed. Many interesting problems remain open.

Original languageEnglish
Pages (from-to)1463-1474
Number of pages12
JournalDiscrete Mathematics
Volume310
Issue number9
DOIs
Publication statusPublished - May 6 2010

Keywords

  • Algorithmic complexity
  • Hypergraph coloring
  • Hypertree
  • Interval hypergraph
  • Mixed hypergraph
  • Stably bounded hypergraph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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