Clique separator decomposition of hole-free and diamond-free graphs and algorithmic consequences
✍ Scribed by Andreas Brandstädt; Vassilis Giakoumakis; Frédéric Maffray
- Book ID
- 113564722
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 231 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
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## Abstract In this paper we investigate the problem of clique‐coloring, which consists in coloring the vertices of a graph in such a way that no monochromatic maximal clique appears, and we focus on odd‐hole‐free graphs. On the one hand we do not know any odd‐hole‐free graph that is not 3‐clique‐c
## Abstract We prove a decomposition theorem for even‐hole‐free graphs. The decompositions used are 2‐joins and star, double‐star and triple‐star cutsets. This theorem is used in the second part of this paper to obtain a polytime recognition algorithm for even‐hole‐free graphs. © 2002 John Wiley &