Israel Journal of Mathematics

, Volume 14, Issue 4, pp 390–408 | Cite as

Acyclic colorings of planar graphs

  • Branko Grünbaum


A coloring of the vertices of a graph byk colors is called acyclic provided that no circuit is bichromatic. We prove that every planar graph has an acyclic coloring with nine colors, and conjecture that five colors are sufficient. Other results on related types of colorings are also obtained; some of them generalize known facts about “point-arboricity”.


Planar Graph Chromatic Number Outerplanar Graph Simple Circuit Distinguished Triangle 
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Copyright information

© Hebrew University 1973

Authors and Affiliations

  • Branko Grünbaum
    • 1
  1. 1.University of WashingtonSeattleU.S.A.

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