MAXIMUM CLIQUE and MINIMUM CLIQUE PARTITION in Visibility Graphs

@inproceedings{Eidenbenz2000MAXIMUMCA,
  title={MAXIMUM CLIQUE and MINIMUM CLIQUE PARTITION in Visibility Graphs},
  author={Stephan Johannes Eidenbenz and Christoph Stamm},
  booktitle={IFIP TCS},
  year={2000}
}
In an alternative approach to "characterizing" the graph class of visibility graphs of simple polygons, we study the problem of finding a maximum clique in the visibility graph of a simple polygon with n vertices. We show that this problem is very hard, if the input polygons are allowed to contain holes: a gap-preserving reduction from the maximum clique problem on general graphs implies that no polynomial time algorithm can achieve an approximation ratio of n1/8-Ɛ/4 for any Ɛ > 0, unless NP… 

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