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 Z3-flow. However, it has been proved that not all such graphs are Z3-connected. In this paper, we show that every 4-edge-connected 2-triangular graph is Z3-connected. The result is best possible. This result provides evidence to support the Z3-connectivity conjecture by Jaeger et al. that every 5-edge-connected graph is Z3-connected.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics