$1$-String $B_2$-VPG Representation of Planar Graphs

TL;DR

This paper proves that all planar graphs can be represented using 1-string B2-VPG representations, where each vertex is a path with at most two bends, intersecting exactly once if connected by an edge.

Contribution

It introduces a universal representation method for planar graphs using 1-string B2-VPG, advancing graph visualization techniques.

Findings

Every planar graph has a 1-string B2-VPG representation.

Paths intersect exactly once for adjacent vertices.

Representation uses at most two bends per path.

Abstract

In this paper, we prove that every planar graph has a 1-string $B_2$-VPG representation---a string representation using paths in a rectangular grid that contain at most two bends. Furthermore, two paths representing vertices $u,v$ intersect precisely once whenever there is an edge between $u$ and $v$.