Coloring plane graphs with independent crossings

Daniel Král͏̌; Ladislav Stacho

doi:10.1002/jgt.20448

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Coloring plane graphs with independent crossings

Daniel Král͏̌Ladislav Stacho

Year: 2009 Journal: Journal of Graph Theory Vol: 64 (3)Pages: 184-205 Publisher: Wiley

DOI: 10.1002/jgt.20448

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Abstract

Abstract We show that every plane graph with maximum face size four in which all faces of size four are vertex‐disjoint is cyclically 5‐colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5‐colorable. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 184–205, 2010

Keywords:

Combinatorics Mathematics Disjoint sets Vertex (graph theory) Plane (geometry) Graph Discrete mathematics Geometry

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Advanced Graph Theory Research

Physical Sciences → Computer Science → Computational Theory and Mathematics

Graph Labeling and Dimension Problems

Physical Sciences → Computer Science → Computational Theory and Mathematics

Computational Geometry and Mesh Generation

Physical Sciences → Computer Science → Computer Graphics and Computer-Aided Design

Coloring plane graphs with independent crossings

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