Year: 2010
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: AT&T (United States), University of Arizona
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951522471