Sparsity of 3-flow critical graphs
Combinatorics
2024-04-02 v1
Abstract
A connected graph G is 3-flow-critical if G does not have a nowhere-zero 3-flow, but every proper contraction of G does. We prove that every n-vertex 3-flow-critical graph other than K_2 and K_4 has at least 5n/3 edges. This bound is tight up to lower-order terms, answering a question of Li et al. (2022). It also generalizes the result of Koester (1991) on the maximum average degree of 4-critical planar graphs.
Keywords
Cite
@article{arxiv.2404.00324,
title = {Sparsity of 3-flow critical graphs},
author = {Zdeněk Dvořák and Sergey Norin},
journal= {arXiv preprint arXiv:2404.00324},
year = {2024}
}
Comments
9 pages, no figures