Israel Journal of Mathematics

, Volume 14, Issue 4, pp 390–408

Acyclic colorings of planar graphs

  • Branko Grünbaum

DOI: 10.1007/BF02764716

Cite this article as:
Grünbaum, B. Israel J. Math. (1973) 14: 390. doi:10.1007/BF02764716


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”.

Copyright information

© Hebrew University 1973

Authors and Affiliations

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