Chordal co-gem-free and (P5,gem)-free graphs have bounded clique-width

  • Authors:

  • Andreas Brandstädt;Hoíng-Oanh Le;Raffaele Mosca

  • Affiliations:

  • Institut für Theoretische Informatik, Fachbereich Informatik, Universität Rostock, Albert-Einstein-Str.21, 18051 Rostock, Germany;Institut für Theoretische Informatik, Fachbereich Informatik, Universität Rostock, Albert-Einstein-Str.21, 18051 Rostock, Germany;Via Latina 7, Pescara 65121, Italy

  • Venue:
  • Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
  • Year:
  • 2005

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Abstract

It is well known that the clique-width of chordal gem-free graphs (also known as ptolemaic graphs), as a subclass of distance-hereditary graphs, is at most 3. Hereby, the gem consists of a P"4 plus a vertex being completely adjacent to the P"4, and the co-gem is its complement graph. On the other hand, unit interval graphs being another important subclass of chordal graphs, have unbounded clique-width. In this note, we show that, based on certain tree structure and module properties, chordal co-gem-free graphs have clique-width at most eight. By a structure result for (P"5,gem)-free graphs, this implies bounded clique-width for this class as well. Moreover, known results on unbounded clique-width of certain grids and of split graphs imply that the gem and the co-gem are the only one-vertex P"4 extension H such that chordal H-free graphs have bounded clique-width.