Nowhere-zero 3-flows in toroidal graphs

Tutte's 3-flow conjecture states that every 4-edge-connected graph admits a nowhere-zero 3-flow. The planar case of Tutte's 3-flow conjecture is the classical Grötzsch's Theorem (1959). Steinberg and Younger (1989) further verified Tutte's 3-flow conjecture for projective planar graphs. In this paper we confirm Tutte's 3-flow conjecture for all toroidal graphs.