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arXiv · 2109.01692

Straight-line Drawings of 1-Planar Graphs

Franz J. Brandenburg
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Abstract

A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line drawing with a two-coloring of the edges, so that edges of the same color do not cross. Hence, 1-planar graphs have geometric thickness two. In addition, each edge is crossed by edges with a common vertex if it is crossed more than twice. The drawings use high precision arithmetic with numbers with O(n log n) digits and can be computed in linear time from a 1-planar drawing

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Franz J. Brandenburg. 2021-09-03. Straight-line Drawings of 1-Planar Graphs. https://arxiv.org/abs/2109.01692

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