The Tree-Width of Clique-Width Bounded Graphs Without Kn, n

  • Authors:
  • Frank Gurski;Egon Wanke

  • Affiliations:
  • -;-

  • Venue:
  • WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
  • Year:
  • 2000

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Abstract

We proof that every graph of clique-width k which does not contain the complete bipartite graph Kn,n for some n 1 as a subgraph has tree-width at most 3k(n - 1) - 1. This immediately implies that a set of graphs of bounded clique-width has bounded tree-width if it is uniformly l-sparse, closed under subgraphs, of bounded degree, or planar.