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On acyclically 4-colorable maximal planar graphs

Author

Listed:
  • Zhu, Enqiang
  • Li, Zepeng
  • Shao, Zehui
  • Xu, Jin

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.

Suggested Citation

  • Zhu, Enqiang & Li, Zepeng & Shao, Zehui & Xu, Jin, 2018. "On acyclically 4-colorable maximal planar graphs," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 402-407.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:402-407
    DOI: 10.1016/j.amc.2018.02.015
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    References listed on IDEAS

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    1. Assefaw H. Gebremedhin & Arijit Tarafdar & Alex Pothen & Andrea Walther, 2009. "Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 209-223, May.
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