On Density of \(\boldsymbol{\mathbb{Z}_3}\) -Flow-Critical Graphs
Zdenĕk Dvořák, Bojan Mohar · SIAM Journal on Discrete Mathematics · 2023
Abstract. For an abelian group [Formula: see text], a graph [Formula: see text] is said to be [Formula: see text]-flow-critical if [Formula: see text] does not admit a nowhere-zero [Formula: see text]-flow, but for each edge [Formula: see text], the contraction [Formula: see text] has a nowhere-zero [Formula: see text]-flow. We obtain a bound on the density of [Formula: see text]-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.