Nowhere-Zero 3-Flows in Squares of Graphs
Rui Xu, Cun‐Quan Zhang · The Electronic Journal of Combinatorics · 2003
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.