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arXiv · 1001.2862

On Touching Triangle Graphs

Emden R. Gansner·Yifan Hu·Stephen G. Kobourov
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Abstract

In this paper, we consider the problem of representing graphs by triangles whose sides touch. As a simple necessary condition, we show that pairs of vertices must have a small common neighborhood. On the positive side, we present linear time algorithms for creating touching triangle representations for outerplanar graphs, square grid graphs, and hexagonal grid graphs. We note that this class of graphs is not closed under minors, making characterization difficult. However, we present a complete characterization of the subclass of biconnected graphs that can be represented as triangulations of some polygon.

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Emden R. Gansner, Yifan Hu, Stephen G. Kobourov. 2010-01-17. On Touching Triangle Graphs. https://arxiv.org/abs/1001.2862

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