On Density of \(\boldsymbol{\mathbb{Z}_3}\) -Flow-Critical Graphs

Abstract

For an abelian group , a graph is said to be -flow-critical if does not admit a nowhere-zero -flow, but for each edge , the contraction has a nowhere-zero -flow. We obtain a bound on the density of -flow-critical graphs drawn on a fixed surface, generalizing the planar case of the bound on the density of 4-critical graphs by Kostochka and Yancey.