On Touching Triangle Graphs

Details On Touching Triangle Graphs On Touching Triangle Graphs

2010-01-17

arxiv.org/abs/1001.2862v1

Computer Science

Discrete Mathematics

13 pages, 9 figures, 19 references, 1 appendix

Scientific paper

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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