On touching triangle graphs. (English) Zbl 1314.68347
Brandes, Ulrik (ed.) et al., Graph drawing. 18th international symposium, GD 2010, Konstanz, Germany, September 21–24, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-18468-0/pbk). Lecture Notes in Computer Science 6502, 250-261 (2011).
Summary: In this paper, we consider the problem of representing graphs by triangles whose sides touch. We present linear time algorithms for creating touching triangles representations for outerplanar graphs, square grid graphs, and hexagonal grid graphs. The class of graphs with touching triangles representations is not closed under minors, making characterization difficult. We do show that pairs of vertices can only have a small common neighborhood, and we present a complete characterization of the subclass of biconnected graphs that can be represented as triangulations of some polygon.
For the entire collection see [Zbl 1206.68006].
For the entire collection see [Zbl 1206.68006].
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
| 05C62 | Graph representations (geometric and intersection representations, etc.) |
| 05C85 | Graph algorithms (graph-theoretic aspects) |
