In a proper edge-coloring of a cubic graph an edge uv is called poor or rich, if the set of colors of the edges incident to u and v contains exactly three or five colors, respectively. An edge-coloring of a graph is normal, if any edge of the graph is either poor or rich. In this note, we show that some snarks constructed by using a method introduced by Loupekhine admit a normal edge-coloring with five colors. The existence of a Berge-Fulkerson Covering for a part of the snarks considered in this paper was recently proved by Manuel and Shanthi (2015). Since the existence of a normal edge-coloring with five colors implies the existence of a Berge-Fulkerson Covering, our main theorem can be viewed as a generalization of their result.

Ferrarini, L., Mazzuoccolo, G., Mkrtchyan, V. (2020). Normal 5-edge-colorings of a family of Loupekhine snarks. AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 17(3), 720-724 [10.1016/j.akcej.2019.12.014].

Normal 5-edge-colorings of a family of Loupekhine snarks

Ferrarini, L;
2020

Abstract

In a proper edge-coloring of a cubic graph an edge uv is called poor or rich, if the set of colors of the edges incident to u and v contains exactly three or five colors, respectively. An edge-coloring of a graph is normal, if any edge of the graph is either poor or rich. In this note, we show that some snarks constructed by using a method introduced by Loupekhine admit a normal edge-coloring with five colors. The existence of a Berge-Fulkerson Covering for a part of the snarks considered in this paper was recently proved by Manuel and Shanthi (2015). Since the existence of a normal edge-coloring with five colors implies the existence of a Berge-Fulkerson Covering, our main theorem can be viewed as a generalization of their result.
Articolo in rivista - Articolo scientifico
class of snarks; Cubic graph; normal edge-coloring; Petersen coloring conjecture;
English
23-apr-2020
2020
17
3
720
724
open
Ferrarini, L., Mazzuoccolo, G., Mkrtchyan, V. (2020). Normal 5-edge-colorings of a family of Loupekhine snarks. AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 17(3), 720-724 [10.1016/j.akcej.2019.12.014].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/402335
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