L. Plachta
Coverings of cubic graphs and 3-edge colorability
Discussiones Mathematicae Graph Theory
Received 18.10.2017, Revised 10.09.2018, Accepted 29.10.2018, doi: 10.7151/dmgt.2194

Let h\colon {\tilde G}→ 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 {\tilde G} is 3-edge uncolorable. As particular cases, we have constructed regular and irregular 5-fold coverings f\colon {\tilde G}→ G of uncolorable cyclically 4-edge connected cubic graphs and an irregular 5-fold covering g\colon {\tilde H}→ H of uncolorable cyclically 6-edge connected cubic graphs. In \cite{S}, 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.
uncolorable cubic graph, covering of graphs, voltage permutation graph, resistance, nowhere-zero 4-flow