Gloria Tabarelli

Let r ≥ 2 $r\ge 2$ be a real number. A complex nowhere-zero r $r$ -flow on a graph G $G$ is an orientation of G $G$ together with an assignment φ : E ( G ) → C $\varphi :E(G)\to {\mathbb{C}}$ such that, for all e ∈ E ( G ) $e\in E(G)$ , the Euclidean norm of the complex number φ ( e ) $\varphi (e)$ lies in the interval [ 1 , r − 1 ] $[1,r-1]$ and, for every vertex, the incoming flow is equal to the outgoing flow.