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Colorings and Homomorphisms of Minor Closed Classes

  • Jaroslav Nešetřil
  • Patrice Ossona de Mendez
Part of the Algorithms and Combinatorics book series (AC, volume 25)

Abstract

We relate acyclic (and star) chromatic number of a graph to the chromatic number of its minors and as a consequence we show that the set of all triangle free planar graphs is homomorphism bounded by a triangle free graph. This solves a problem posed in [[15]]. It also improves the best known bound for the star chromatic number of planar graphs from 80 to 30. Our method generalizes to all minor closed classes and puts Hadwiger conjecture in yet another context.

Keywords

Planar Graph Chromatic Number Proper Coloring Mixed Graph Acyclic Orientation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jaroslav Nešetřil
    • 1
  • Patrice Ossona de Mendez
    • 2
  1. 1.Department of Applied Mathematics and Institute of Theoretical Computer Science (ITI)Charles UniversityPraha 1Czech Republic
  2. 2.Centre d’Analyse et de Mathématiques Sociales (UMR 8557), CNRSParisFrance

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