On Touching Triangle Graphs
Discrete Mathematics
2010-01-19 v1 Data Structures and Algorithms
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.
Cite
@article{arxiv.1001.2862,
title = {On Touching Triangle Graphs},
author = {Emden R. Gansner and Yifan Hu and Stephen G. Kobourov},
journal= {arXiv preprint arXiv:1001.2862},
year = {2010}
}
Comments
13 pages, 9 figures, 19 references, 1 appendix