Sparsity of 3-flow critical graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913292692226048 |
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| author | Dvořák, Zdeněk Norin, Sergey |
| author_facet | Dvořák, Zdeněk Norin, Sergey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparsity of 3-flow critical graphs Dvořák, Zdeněk Norin, Sergey Combinatorics 05C21 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. |
| title | Sparsity of 3-flow critical graphs |
| topic | Combinatorics 05C21 |
| url | https://arxiv.org/abs/2404.00324 |