Conflict-free colouring of graphs

Roman Glebov, Tibor Szabó, G. Tardos

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We study the conflict-free chromatic number χ CF of graphs from extremal and probabilistic points of view. We resolve a question of Pach and Tardos about the maximum conflict-free chromatic number an n-vertex graph can have. Our construction is randomized. In relation to this we study the evolution of the conflict-free chromatic number of the ErdÅ's-Rényi random graph G(n,p) and give the asymptotics for p = ω(1/n). We also show that for p ≥ 1/2 the conflict-free chromatic number differs from the domination number by at most 3.

Original languageEnglish
Pages (from-to)434-448
Number of pages15
JournalCombinatorics Probability and Computing
Volume23
Issue number3
DOIs
Publication statusPublished - 2014

Fingerprint

Coloring
Chromatic number
Colouring
Graph in graph theory
Domination number
Random Graphs
Resolve
Conflict
Vertex of a graph

Keywords

  • 05C69
  • 05C80
  • 05D40
  • 2010 Mathematics subject classification: Primary 05C15
  • Secondary 05C35

ASJC Scopus subject areas

  • Applied Mathematics
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Statistics and Probability

Cite this

Conflict-free colouring of graphs. / Glebov, Roman; Szabó, Tibor; Tardos, G.

In: Combinatorics Probability and Computing, Vol. 23, No. 3, 2014, p. 434-448.

Research output: Contribution to journalArticle

Glebov, Roman ; Szabó, Tibor ; Tardos, G. / Conflict-free colouring of graphs. In: Combinatorics Probability and Computing. 2014 ; Vol. 23, No. 3. pp. 434-448.
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