On Visibility Representation of Plane Graphs

In a visibility representation (VR for short) of a plane graph G, each vertex of G is represented by a horizontal line segment such that the line segments representing any two adjacent vertices of G are joined by a vertical line segment. Rosenstiehl and Tarjan [11], Tamassia and Tollis [14] independently gave linear time VR algorithms for 2-connected plane graph. Recently, Lin et. al. reduced the width bound to \(\lfloor \frac{22n - 42}{15} \rfloor\) [10]. In this paper, we prove that any plane graph G has a VR with width at most \(\lfloor \frac{13n - 24}{9} \rfloor\).

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