Which k-trees are cover-incomparability graphs?

  • Authors:

  • Jana Maxová;Miroslava Dubcová;Pavla Pavlíková;Daniel Turzík

  • Affiliations:

  • -;-;-;-

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2014

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Abstract

In this paper we deal with cover-incomparability graphs of posets. It is known that the class of cover-incomparability graphs is not closed on induced subgraphs which makes the study of structural properties of these graphs difficult. In this paper we introduce the notion of s-subgraph which enables us to define forbidden s-subgraphs (i.e. graphs that cannot appear as s-subgraphs of any cover-incomparability graph). We show that the family of minimal forbidden s-subgraphs is infinite even for cover-incomparability unit-interval graphs. Using the notion of s-subgraph we also answer the question which k-trees are cover-incomparability graphs and which chordal graphs without K"4 are cover-incomparability graphs.