# On acyclically 4-colorable maximal planar graphs

On acyclically 4-colorable maximal planar graphs An acyclic coloring of a graph is a proper coloring of the graph, for which every cycle uses at least three colors. Let G4 be the set of maximal planar graphs of minimum degree 4, such that each graph in G4 contains exactly four odd-vertices and the subgraph induced by the four odd-vertices contains a quadrilateral. In this article, we show that every acyclic 4-coloring of a maximal planar graph with exact four odd-vertices is locally equitable with regard to its four odd-vertices. Moreover, we obtain a necessary and sufficient condition for a graph in G4 to be acyclically 4-colorable, and give an enumeration of the acyclically 4-colorable graphs in G4. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

# On acyclically 4-colorable maximal planar graphs

, Volume 329 – Jul 15, 2018
6 pages

/lp/elsevier/on-acyclically-4-colorable-maximal-planar-graphs-dRL7TTApIx
Publisher
Elsevier
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.02.015
Publisher site
See Article on Publisher Site

### Abstract

An acyclic coloring of a graph is a proper coloring of the graph, for which every cycle uses at least three colors. Let G4 be the set of maximal planar graphs of minimum degree 4, such that each graph in G4 contains exactly four odd-vertices and the subgraph induced by the four odd-vertices contains a quadrilateral. In this article, we show that every acyclic 4-coloring of a maximal planar graph with exact four odd-vertices is locally equitable with regard to its four odd-vertices. Moreover, we obtain a necessary and sufficient condition for a graph in G4 to be acyclically 4-colorable, and give an enumeration of the acyclically 4-colorable graphs in G4.

### Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

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