Strongly even cycle decomposable non-planar line graphs.

A graph G is strongly even cycle decomposable if for every subdivision G ′ of G with an even number of edges, the edges of G ′ can be partitioned into cycles of even length. Máčajová and Mazák asked whether the line graph of a simple 2-connected cubic graph is strongly even cycle decomposable. A result of Seymour implies that the line graph of every 2-connected planar cubic graph is strongly even cycle decomposable. In this paper, we prove that the line graphs of simple 3-connected cubic graphs embedded in the projective plane or in the torus are strongly even cycle decomposable. [ABSTRACT FROM AUTHOR]