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arXiv · 1307.1169

Convex geometric (k+2)-quasiplanar representations of semi-bar k-visibility graphs

Jesse Geneson·Tanya Khovanova·Jonathan Tidor
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Abstract

We examine semi-bar visibility graphs in the plane and on a cylinder in which sightlines can pass through k objects. We show every semi-bar k-visibility graph has a (k+2)-quasiplanar representation in the plane with vertices drawn as points in convex position and edges drawn as segments. We also show that the graphs having cylindrical semi-bar k-visibility representations with semi-bars of different lengths are the same as the (2k+2)-degenerate graphs having edge-maximal (k+2)-quasiplanar representations in the plane with vertices drawn as points in convex position and edges drawn as segments.

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Jesse Geneson, Tanya Khovanova, Jonathan Tidor. 2013-07-03. Convex geometric (k+2)-quasiplanar representations of semi-bar k-visibility graphs. https://arxiv.org/abs/1307.1169

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