Approximating Domination on Intersection Graphs of Paths on a Grid

A graph G is called \({B}_k\)-EPG (resp., \({B}_k\)-VPG), for some constant \(k\ge 0\), if it has a string representation on an axis-parallel grid such that each vertex is a path with at most k bends and two vertices are adjacent in G if and only if the corresponding strings share at least one grid edge (resp., the corresponding strings intersect each other). If two adjacent strings of a B\(_k\)-VPG graph intersect each other exactly once, then the graph is called a one-string B\(_k\)-VPG graph.

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