Compatible Euler Tours and Supplementary Eulerian Vectors

Two Euler tours of a graph G are compatible if no pair of adjacent edges of G are consecutive in both tours. Bill Jackson recently gave a good characterization of those 4-regular graphs which contain three pairwise compatible Euler tours. In this paper we give a solution by means of a polynomial-time algorithm, and we give a min-max relation generalizing Jacksonʹs theorem. The solution uses the theory of isotropic systems by replacing Euler tours by supplementary Eulerian vectors.