Gallai colorings of non-complete graphs

András Gyárfás, Gábor N. Sárközy

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Gallai-colorings of complete graphs-edge colorings such that no triangle is colored with three distinct colors-occur in various contexts such as the theory of partially ordered sets (in Gallai's original paper), information theory and the theory of perfect graphs. We extend here Gallai-colorings to non-complete graphs and study the analogue of a basic result-any Gallai-colored complete graph has a monochromatic spanning tree-in this more general setting. We show that edge colorings of a graph H without multicolored triangles contain monochromatic connected subgraphs with at least (α (H)2 + α (H) - 1)- 1 | V (H) | vertices, where α (H) is the independence number of H. In general, we show that if the edges of an r-uniform hypergraph H are colored so that there is no multicolored copy of a fixed F then there is a monochromatic connected subhypergraph H1 ⊆ H such that | V (H1) | ≥ c | V (H) | where c depends only on F, r, and α (H).

Original languageEnglish
Pages (from-to)977-980
Number of pages4
JournalDiscrete Mathematics
Volume310
Issue number5
DOIs
Publication statusPublished - Mar 6 2010

Keywords

  • Gallai colorings
  • Monochromatic connected components

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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