Trees in greedy colorings of hypergraphs

A. Gyárfás, Jenö Lehel

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is a well-known proposition that every graph of chromatic number larger than t contains every tree with t edges. The 'standard' reasoning is that such a graph must contain a subgraph of minimum degree at least t. Bohman, Frieze, and Mubayi noticed that, although this argument does not work for hypergraphs, it is still possible that the proposition holds for hypergraphs as well. Indeed, Loh recently proved that every uniform hypergraph of chromatic number larger than t contains every hypertree with t edges. Here we observe that the basic property of the well-known greedy algorithm immediately implies a much more general result (with a conceptually simpler proof): if the greedy algorithm colors the vertices of an r-uniform hypergraph with more than t colors then the hypergraph contains every r-uniform hypertree with t edges.

Original languageEnglish
Pages (from-to)208-209
Number of pages2
JournalDiscrete Mathematics
Volume311
Issue number2-3
DOIs
Publication statusPublished - Feb 6 2011

Fingerprint

Coloring
Hypergraph
Hypertree
Colouring
Uniform Hypergraph
Greedy Algorithm
Chromatic number
Color
Proposition
Minimum Degree
Graph in graph theory
Immediately
Subgraph
Reasoning
Imply

Keywords

  • Chromatic number
  • Greedy coloring
  • Subtrees in graphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Trees in greedy colorings of hypergraphs. / Gyárfás, A.; Lehel, Jenö.

In: Discrete Mathematics, Vol. 311, No. 2-3, 06.02.2011, p. 208-209.

Research output: Contribution to journalArticle

Gyárfás, A. ; Lehel, Jenö. / Trees in greedy colorings of hypergraphs. In: Discrete Mathematics. 2011 ; Vol. 311, No. 2-3. pp. 208-209.
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