2016/11/07 by Hasanvand, Morteza
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1611.02231
Tutte's 3-flow conjecture says that every 4-edge-connected graph admits a nowhere-zero 3-flow. Kochol (2001) showed that it is enough to prove this conjecture for 5-edge-connected graphs. Former, Jaeger, Linial, Payan, and Tarsi (1992) conjectured that every 5-edge-connected graph is Z3-connected and so it admits a nowhere-zero 3-flow. In this note, we show that if the second conjecture would be true, then every 3-tree-connected graph must also be Z3-connected and so Tutte's 3-flow conjecture can be extended to this family of graphs.