Splitting \(B_2\)-VPG Graphs into Outer-String and Co-Comparability Graphs
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A \(B_2\)-VPG representation of a graph is an intersection representation that consists of orthogonal curves with at most 2 bends. In this paper, we show that the curves of such a representation can be partitioned into \(O(\log n)\) groups that represent outer-string graphs or \(O(\log ^3 n)\) groups that represent permutation graphs. This leads to better approximation algorithms for hereditary graph problems, such as independent set, clique and clique cover, on \(B_2\)-VPG graphs.
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- 1.Cardinal, J., Felsner, S., Miltzow, T., Tompkins, C., Vogtenhuber, B.: Intersection graphs of rays and grounded segments. Technical Report 1612.03638 [cs.DM], ArXiV (2016)Google Scholar
- 3.Fox, J., Pach, J.: Computing the independence number of intersection graphs. In: Randall, D. (ed.) Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, January 23–25, pp. 1161–1165. SIAM (2011)Google Scholar
- 4.Golumbic, M.C.: Algorithmic graph theory and perfect graphs, 1st edn. Academic Press, New York (1980)Google Scholar