The Geometric Thickness of Low Degree Graphs
Computational Geometry
2007-05-23 v1 Discrete Mathematics
Abstract
We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. All of our algorithms run in O(n) time, where n is the number of vertices in the graph. In our proofs, we present an embedding algorithm for graphs with maximum degree three that uses an n x n grid and a more complex algorithm for embedding a graph with maximum degree four. We also show a variation using orthogonal edges for maximum degree four graphs that also uses an n x n grid. The results have implications in graph theory, graph drawing, and VLSI design.
Cite
@article{arxiv.cs/0312056,
title = {The Geometric Thickness of Low Degree Graphs},
author = {Christian A. Duncan and David Eppstein and Stephen G. Kobourov},
journal= {arXiv preprint arXiv:cs/0312056},
year = {2007}
}
Comments
10 pages, 7 figures, submitted to SoCG 2004