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The following open problem was proposed by Archdeacon: Characterize all graphical sequences π such that some realization of π admits a nowhere-zero 3-flow. The purpose of this paper is to resolve this problem and present a complete characterization: A graphical sequence π = (d1, d2, ., dn) with minimum degree at least two has a realization that admits a nowhere-zero 3-flow if and only if π ≠ (34, 2), (k, 3k), (k2, 3k―1), where k is an odd integer.

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Luo, Rong., Xu, Rui., Zang, Wenan., & Zhang, Cun-Quan. (2008). Realizing Degree Sequences With Graphs Having Nowhere-Zero 3-Flows. SIAM Journal on Discrete Mathematics, 22(2), 500-519.