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Reduction Operations and Characterizations of $S^1$-Flows in Graphs
Thomassen (J. Combin. Theory Ser. B 108 (2014), 81-91) showed that every graph admitting a nowhere-zero $3$-flow also admits an $S^1$-flow. He also proved that the converse holds for cubic graphs, but constructed counterexamples showing it fails in general. Wang et al. (SIAM J. Discrete Math. 29 (20
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