Nowhere-Zero 3-Flows in Squares of Graphs

Rui Xu, Cun-Quan Zhang


It was conjectured by Tutte that every 4-edge-connected graph admits a nowhere-zero $3$-flow. In this paper, we give a complete characterization of graphs whose squares admit nowhere-zero $3$-flows and thus confirm Tutte's $3$-flow conjecture for the family of squares of graphs.

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