# tension

## 5-local-tensions ★★

Author(s): DeVos

\begin{conjecture} There exists a fixed constant $c$ (probably $c=4$ suffices) so that every embedded (loopless) graph with edge-width $\ge c$ has a 5-local-tension. \end{conjecture}

Keywords: coloring; surface; tension

## A homomorphism problem for flows ★★

Author(s): DeVos

\begin{conjecture} Let $M,M'$ be abelian groups and let $B \subseteq M$ and $B' \subseteq M'$ satisfy $B=-B$ and $B' = -B'$. If there is a \Def[homomorphism]{graph homomorphism} from $Cayley(M,B)$ to $Cayley(M',B')$, then every graph with a B-flow has a B'-flow. \end{conjecture}

Keywords: homomorphism; nowhere-zero flow; tension