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The Geometric Thickness of Low Degree Graphs

Christian A. Duncan·David Eppstein·Stephen G. Kobourov
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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.

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BibTeXRIS

Christian A. Duncan, David Eppstein, Stephen G. Kobourov. 2003-12-24. The Geometric Thickness of Low Degree Graphs. https://arxiv.org/abs/cs/0312056

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