Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero Z3-flow and Jaeger et al. [Group connectivity of graphs–a nonhomogeneous analogue of nowhere-zero flow properties, J. Combin. Theory Ser. B 56 (1992) 165-182] further conjectured that every 5-edge-connected graph isZ3-connected.These two conjectures are in general open and few results are known so far. Aweaker version of ...

Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction cubic graphs. In this paper, we proved 3-edge-colorable 10-flow. This together with 4-color theorem implies bridgeless planar As byproduct, also show hamiltonian 8-flow.

A sufficient condition for graphs with circular flow index less than 4 is found in this paper. In particular, we give a simple proof of a result obtained by Galluccio and Goddyn (Combinatorica, 2002), and obtain a larger family of such graphs. We refer readers to [1], [2] and [7] for the standard terminology and notations in this paper. The following theorem was proved by Galluccio and Goddyn. ...

We present a tool that shows, that the existence of a k-nowhere-zero-flow is compatible with 1-,2and 3-sums in regular matroids. As application we present a conjecture for regular matroids that is equivalent to Hadwiger’s conjecture for graphs and Tuttes’s 4and 5-flow conjectures.