On density of $Z_3$-flow-critical graphs

Zdeněk Dvořák, Bojan Mohar

Published 2022-05-16Version 1

For an abelian group $\Gamma$, a graph $G$ is said to be $\Gamma$-flow-critical if $G$ does not admit a nowhere-zero $\Gamma$-flow, but for each edge $e\in E(G)$, the contraction $G/e$ has a nowhere-zero $\Gamma$-flow. A bound on the density of $Z_3$-flow-critical graphs drawn on a fixed surface is obtained, generalizing the bound on the density of 4-critical graphs by Kostochka and Yancey.