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 Grotzsch'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. (c) 2021 Elsevier Inc. All rights reserved.
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