Classes of graphs with small rank decompositions are Χ-bounded

  • Authors:

  • Zdenk Dvořák;Daniel Král'

  • Affiliations:

  • Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Faculty of Mathematics and Physics, Charles University, Malostranské nám.25, 118 00 Prague, Czech ...;Department of Mathematics, University of West Bohemia, Univerzitní 8, 306 14 Pilsen, Czech Republic

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2012

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Abstract

A class of graphs G is @g-bounded if the chromatic number of graphs in G is bounded by a function of the clique number. We show that if a class G is @g-bounded, then every class of graphs admitting a decomposition along cuts of small rank to graphs from G is @g-bounded. As a corollary, we obtain that every class of graphs with bounded rank-width (or equivalently, clique-width) is @g-bounded.