Add to ORKGTutte's 3-flow conjecture is restated as the problem of finding an orientation of the edges of a 4-edge-connected, 5-regular graph G, for which the out-flow at each vertex is +3 or -3. The induced equipartition of the vertices of G is called mod 3-orientable. We give necessary and sufficient conditions for the existence of mod 3-orientable equipartitions in general 5-regular graphs, in terms of (i) a perfect matching of a bipartite graph derived from the equipartition and (ii) the size of cuts in G.7114117Bondy, J.A., Murty, U.S.R., (1976) Graph Theory with Applications, , Elsevier North HollandDe Almeida E Silva, L.M., (1991) Fluxos Inteiros Em Grafos, , Master's thesis, UNICAMPYounger, D.H., Integer Flows (1983) J. Graph Theory, 7, pp. 34...