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.
Digital Commons Citation
Luo, Rong; Xu, Rui; Zang, Wenan; and Zhang, Cun-Quan, "Realizing Degree Sequences with Graphs Having Nowhere-Zero 3-Flows" (2008). Faculty & Staff Scholarship. 307.
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. http://doi.org/10.1137/070687372