Opuscula Math. 38, no. 6 (2018), 819-827

Opuscula Mathematica

Zig-zag facial total-coloring of plane graphs

Július Czap
Stanislav Jendroľ
Margit Voigt

Abstract. In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain lower and upper bounds for the minimum number of colors which is necessary for such a coloring. Moreover, we give several sharpness examples and formulate some open problems.

Keywords: plane graph, facial coloring, total-coloring, zig-zag coloring.

Mathematics Subject Classification: 05C10, 05C15.

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  • Július Czap
  • Technical University of Košice, Department of Applied Mathematics and Business Informatics, Faculty of Economics, Němcovej 32, 04001 Košice, Slovakia
  • Stanislav Jendroľ
  • P.J. Šafárik University, Institute of Mathematics, Jesenná 5, 04001 Košice, Slovakia
  • Margit Voigt
  • University of Applied Sciences Dresden, Faculty of Informatics and Mathematics, Friedrich-List-Platz 1, 01069 Dresden, Germany
  • Communicated by Adam Paweł Wojda.
  • Received: 2018-01-24.
  • Revised: 2018-02-13.
  • Accepted: 2018-02-15.
  • Published online: 2018-07-05.
Opuscula Mathematica - cover

Cite this article as:
Július Czap, Stanislav Jendroľ, Margit Voigt, Zig-zag facial total-coloring of plane graphs, Opuscula Math. 38, no. 6 (2018), 819-827, https://doi.org/10.7494/OpMath.2018.38.6.819

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