Abstract
A graph is a quasi-line graph if for every vertex v, the set of neighbours of v is expressible as the union of two cliques. Such graphs are more general than line graphs, but less general than claw-free graphs. Here we give a construction for all quasi-line graphs; it turns out that there are basically two kinds of connected quasi-line graphs, one a generalization of line graphs, and the other a subclass of circular arc graphs.
Original language | English (US) |
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Pages (from-to) | 1267-1294 |
Number of pages | 28 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 102 |
Issue number | 6 |
DOIs | |
State | Published - Nov 2012 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
Keywords
- Claw-free
- Induced subgraph
- Quasi-line
- Structure theorem