Abstract
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 Jackson's theorem. The solution uses the theory of isotropic systems by replacing Euler tours by supplementary Eulerian vectors.
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