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 language | English (US) |
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Pages (from-to) | 249-290 |
Number of pages | 42 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 98 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2008 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
Keywords
- Claw-free graphs
- Induced subgraphs