In this paper, we prove that if an 8-edge-connected signed graph admits a nowhere-zero integer flow, then it has a nowhere-zero 3-flow. Our result extends ...

Aug 29, 2019 · Abstract:Many basic properties in Tutte's flow theory for unsigned graphs do not have their counterparts for signed graphs.

For example, the unsigned Petersen graph admits a nowhere-zero 5-flow, while the signed Petersen graph of Figure 1, which has no long barbells, admits a nowhere ...

However, some element (long barbells) in the cycle space of a signed graph is the support of a 3-flow but not a 2-flow. Therefore, we may expect signed graphs.

However, signed graphs without long barbells in many ways behave like unsigned graphs from the point view of flows. In this paper, we study whether some basic ...

The equality of the integer flow number and the ceiling of the circular flow number for flow-admissible signed graphs without long barbells is proved.

In this paper, we study whether some basic properties in Tutte's flow theory remain valid for this family of signed graphs. Specifically let $(G,\sigma)$ be a ...

Many basic properties in Tutte's flow theory for unsigned graphs do not have their counterparts for signed graphs. However, signed graphs without long ...

A signed graph G is a graph associated with a mapping σ: E(G)→(+1,-1). An edge eεE(G) is positive if σ(e)=1 and negative if σ(e)=-1. A circuit in G is balanced ...

The following lemma converts a modulo flow to an integer-valued flow if G does not contain long barbells. Lemma 1.4.10. (Lu et al. [16]) Let (G, σ) be a signed ...