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.
Digital Commons Citation
Xu, Rui and Zhang, Cun-Quan, "Nowhere-Zero 3-Flows in Squares of Graphs" (2003). Faculty Scholarship. 254.
Xu, Rui., &Zhang, Cun-Quan. (2003). Nowhere-Zero 3-Flows In Squares Of Graphs. The Electronic Journal of Combinatorics, 10(1), 5.