Bar 1-Visibility Drawings of 1-Planar Graphs
Shaheena Sultana, Md. Saidur Rahman, Arpita Roy, Suraiya, Tairin

TL;DR
This paper introduces linear-time algorithms for creating bar 1-visibility drawings of certain 1-planar graphs, expanding understanding of graph visualization techniques for these classes.
Contribution
It provides the first linear-time algorithms for bar 1-visibility drawings of diagonal grid and maximal outer 1-planar graphs, and proves other classes are bar 1-visible.
Findings
Linear-time algorithms for diagonal grid graphs and maximal outer 1-planar graphs.
Recursive quadrangle and pseudo double wheel 1-planar graphs are bar 1-visible.
Enhanced understanding of graph visualization for 1-planar graphs.
Abstract
A bar 1-visibility drawing of a graph is a drawing of 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 is bar 1-visible if has a bar 1-visibility drawing. A graph is 1-planar if 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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Taxonomy
TopicsComputational Geometry and Mesh Generation · 3D Modeling in Geospatial Applications · Computer Graphics and Visualization Techniques
