# Jain, Kamal

## Unit vector flows ★★

Author(s): Jain

\begin{conjecture} For every graph $G$ without a \Def[bridge]{bridge (graph theory)}, there is a flow $\phi : E(G) \rightarrow S^2 = \{ x \in {\mathbb R}^3 : |x| = 1 \}$.

\end{conjecture}

\begin{conjecture} There exists a map $q:S^2 \rightarrow \{-4,-3,-2,-1,1,2,3,4\}$ so that antipodal points of $S^2$ receive opposite values, and so that any three points which are equidistant on a great circle have values which sum to zero. \end{conjecture}

Keywords: nowhere-zero flow