Geodesic
Coverings of Cubic Graphs and 3-Edge Colorability
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 311-334

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Let h:G̃→G be a finite covering of 2-connected cubic (multi)graphs where G is 3-edge uncolorable. In this paper, we describe conditions under which G̃ is 3-edge uncolorable. As particular cases, we have constructed regular and irregular 5-fold coverings f:G̃→G of uncolorable cyclically 4-edge connected cubic graphs and an irregular 5-fold covering g:H̃→H of uncolorable cyclically 6-edge connected cubic graphs. In [13], Steffen introduced the resistance of a subcubic graph, a characteristic that measures how far is this graph from being 3-edge colorable. In this paper, we also study the relation between the resistance of the base cubic graph and the covering cubic graph.
Keywords: uncolorable cubic graph, covering of graphs, voltage permutation graph, resistance, nowhere-zero 4-flow 
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Plachta, Leonid. Coverings of Cubic Graphs and 3-Edge Colorability. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 311-334. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a19/