Every Planar Map is Four Colorable

1989/01/01 by Kenneth E. Appel, Wolfgang Haken · 8 citations
Computer Science · #Computational Geometry and Mesh Generation #Graph Labeling and Dimension Problems

paper · doi:10.1090/conm/098

openalex publication_date 1989/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The following theorem is proved.THEOREM .Every planar map can be colored with at most four colors.

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• Complexity of 3-edge-coloring in the class of cubic graphs with a polyhedral embedding in an orientable surface
• Organizing volumes of right-angled hyperbolic polyhedra
• Even-cycle decompositions of graphs with no odd-K4-minor
• 20th century [wikipedia]
• Four color theorem [wikipedia]
• Snark (graph theory) [wikipedia]