Strongly even cycle decomposable 4-regular line graphs (Part I)

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, i.e., G' admits an even cycle decomposition. Markström conjectured that for any simple 2-connected cubic graph G, its line graph L(G) is even cycle decomposable. Máčajová and Mazák further asked whether L(G) is strongly even cycle decomposable. Clearly, the affirmative answer to Máčajová and Mazák’s problem implies Markström conjecture. In this series of talks, we introduce our recent results on Máčajová and Mazák’s question (as well as Markström’s conjecture).