Splitting \(B_2\)-VPG Graphs into Outer-String and Co-Comparability Graphs
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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