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A linear upper bound on the rectilinear crossing number

By David R. Wood

Abstract

It is proved that the rectilinear crossing number of every graph with bounded tree-width and bounded degree is linear in the number of vertices. **** This paper has been withdrawn by the author. **** The results have been superseeded by the author's paper with Jan Arne Telle: "Planar decompositions and the crossing number of graphs with an excluded minor", http://arxiv.org/math/0604467.Comment: This paper has been withdrawn by the author. The results have been superseeded by the author's paper with Jan Arne Telle: "Planar decompositions and the crossing number of graphs with an excluded minor", http://arxiv.org/math/060446

Topics: Mathematics - Combinatorics, 05C10
Year: 2006
OAI identifier: oai:arXiv.org:math/0512392
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