Claw-free graphs. II. Non-orientable prismatic graphs

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Abstract

A graph is prismatic if for every triangle T, every vertex not in T has exactly one neighbour in T. In a previous paper we gave a complete description of all 3-colourable prismatic graphs, and of a slightly more general class, the "orientable" prismatic graphs. In this paper we describe the non-orientable ones, thereby completing a description of all prismatic graphs. Since complements of prismatic graphs are claw-free, this is a step towards the main goal of this series of papers, providing a structural description of all claw-free graphs (a graph is claw-free if no vertex has three pairwise nonadjacent neighbours).

Original languageEnglish (US)
Pages (from-to)249-290
Number of pages42
JournalJournal of Combinatorial Theory. Series B
Volume98
Issue number2
DOIs
StatePublished - Mar 1 2008

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Claw-free graphs
  • Induced subgraphs

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