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

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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About the authors ▼
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
About the article ▼
Communicated by Adam Paweł Wojda.
Received: 2018-01-24.
Revised: 2018-02-13.
Accepted: 2018-02-15.
Published online: 2018-07-05.
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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