6 research outputs found
Drawings of Planar Graphs with Few Slopes and Segments
We study straight-line drawings of planar graphs with few segments and few
slopes. Optimal results are obtained for all trees. Tight bounds are obtained
for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every
3-connected plane graph on vertices has a plane drawing with at most
segments and at most slopes. We prove that every cubic
3-connected plane graph has a plane drawing with three slopes (and three bends
on the outerface). In a companion paper, drawings of non-planar graphs with few
slopes are also considered.Comment: This paper is submitted to a journal. A preliminary version appeared
as "Really Straight Graph Drawings" in the Graph Drawing 2004 conference. See
http://arxiv.org/math/0606446 for a companion pape
Collection of abstracts of the 24th European Workshop on Computational Geometry
International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop
Intersection Graphs of Jordan Arcs
A family of Jordan arcs, such that two arcs are nowhere tangent, defines a hypergraph whose vertices are the arcs and whose edges are the intersection points. We shall say that the hypergraph has a strong intersection representation and, if each intersection point is interior to at most one arc, we shall say that the hypergraph has a strong contact representation. We first characterize those hypergraphs which have a strong contact representation and deduce some sufficient conditions for a simple planar graph to have a strong intersection representation. Then, using the Four Color Theorem, we prove that a large class of simple planar graphs have a strong intersection representation
Intersection Graphs of Jordan Arcs
. A family of Jordan arcs, such that two arcs are nowhere tangent, defines a hypergraph whose vertices are the arcs and whose edges are the intersection points. We shall say that the hypergraph has a strong intersection representation and, if each intersection point is interior to at most one arc, we shall say that the hypergraph has a strong contact representation. We first characterize those hypergraphs which have a strong contact representation and deduce some sufficient conditions for a simple planar graph to have a strong intersection representation. Then, using the Four Color Theorem, we prove that a large class of simple planar graphs have a strong intersection representation. 1. Introduction A family of Jordan arcs, such that two arcs are nowhere tangent, defines a hypergraph whose vertices are the arcs and whose edges are the intersection points. We shall say that the hypergraph has a strong intersection representation and, if each intersection point is interior to at most o..