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arXiv · 1302.4870

Bar 1-Visibility Drawings of 1-Planar Graphs

Shaheena Sultana·Md. Saidur Rahman·Arpita Roy·Suraiya Tairin
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Abstract

A bar 1-visibility drawing of a graph $G$ is a drawing of $G$ where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment where the vertical line segment representing an edge must connect the horizontal line segments representing the end vertices and a vertical line segment corresponding to an edge intersects at most one bar which is not an end point of the edge. A graph $G$ is bar 1-visible if $G$ has a bar 1-visibility drawing. A graph $G$ is 1-planar if $G$ has a drawing in a 2-dimensional plane such that an edge crosses at most one other edge. In this paper we give linear-time algorithms to find bar 1-visibility drawings of diagonal grid graphs and maximal outer 1-planar graphs. We also show that recursive quadrangle 1-planar graphs and pseudo double wheel 1-planar graphs are bar 1-visible graphs.

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Shaheena Sultana, Md. Saidur Rahman, Arpita Roy, Suraiya Tairin. 2013-02-20. Bar 1-Visibility Drawings of 1-Planar Graphs. https://arxiv.org/abs/1302.4870

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