Z3-connectivity of 4-edge-connected 2-triangular graphs

A graph G is k -triangular if each edge of G is in at least k triangles. It is conjectured that every 4 -edge-connected 1-triangular graph admits a nowhere-zero Z 3 -flow. However, it has been proved that not all such graphs are Z 3 -connected. In this paper, we show that every 4 -edge-connected 2-triangular graph is Z 3 -connected. The result is best possible. This result provides evidence to support the Z 3 -connectivity conjecture by Jaeger et al that every 5-edge-connected graph is Z 3 -connected.