Zig-zag facial total-coloring of plane graphs

• Autorzy: Czap J. , Jendrol S. , Voigt M.

Identyfikatory

DOI

10.7494/OpMath.2018.38.6.819

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

plane graph; facial coloring total-coloring zig-zag coloring

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 6
• Strony: 819--827
• Opis fizyczny: BIbliogr. 11 poz.

Twórcy

autor

Czap J.

• Technical University of Kosice, Department of Applied Mathematics and Business Informatics Faculty of Economics Nemcovej 32, 04001 Kosice, Slovakia

autor

Jendrol S.

• P.J. Šafárik University Institute of Mathematics Jesenná 5, 04001 Košice, Slovakia

autor

Voigt M.

• University of Applied Sciences Dresden Faculty of Informatics and Mathematics Friedrich-List-Platz 1, 01069 Dresden, Germany

Bibliografia

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• [3] R.L. Brooks, On colouring the nodes of a network, Proc. Cambridge Philosophical Society, Math. Phys. Sci. 37 (1941), 194-197.
• [4] J. Czap, S. Jendrol', Facially-constrained colorings of plane graphs: A survey, Discrete Math. 340 (2017), 2691-2703.
• [5] J. Czap, P. Śugerek, Facial total-coloring of bipartite plane graphs, Int. J. Pure Appl. Math. 115 (2017), 115-121.
• [6] I. Fabrici, S. Jendrol, M. Vrbjarova, Facial entire colouring of plane graphs, Discrete Math. 339 (2016), 626-631.
• [7] I. Fabrici, S. Jendrol, M. Voigt, Facial list colourings of plane graphs, Discrete Math. 339 (2016), 2826-2831.
• [8] H. Grótzsch, Ein Dreifarbensatz fur dreikreisfreie Netze auf der Kugel, Wiss. Z. Martin Luther-Universitat, Halle, Wittenberg, Math.-Nat. Reihe 8 (1959), 109-120.
• [9] S. Kitaev, Patterns in permutations and words, Springer, 2011.
• [10] T.L. Saaty, P.C. Kainen, The Four-Color Problem, Assaults and Conquest, McGraw-Hill, 1977.
• [11] P.G. Tait, Remarks on the colouring of maps, Proc. Roy. Soc. Edinburgh 10 (1880), 729.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).