Acyclic colorings of planar graphs

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”. Research supported in part by the Office of Naval Research under Grant N00014-67-A-0103-0003.