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arXiv · 1702.05265

T-Shape Visibility Representations of 1-Planar Graphs

Franz J. Brandenburg
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Abstract

A shape visibility representation displays a graph so that each vertex is represented by an orthogonal polygon of a particular shape and for each edge there is a horizontal or vertical line of sight between the polygons assigned to its endvertices. Special shapes are rectangles, L, T, E and H-shapes, and caterpillars. A flat rectangle is a horizontal bar of height $\epsilon>0$. A graph is 1-planar if there is a drawing in the plane such that each edge is crossed at most once and is IC-planar if in addition no two crossing edges share a vertex. We show that every IC-planar graph has a flat rectangle visibility representation and that every 1-planar graph has a T-shape visibility representation. The representations use quadratic area and can be computed in linear time from a given embedding.

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Franz J. Brandenburg. 2017-02-17. T-Shape Visibility Representations of 1-Planar Graphs. https://doi.org/10.1016/j.comgeo.2017.10.007

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