Sparsity of 3-flow-critical graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511828" target="_blank" >RIV/00216208:11320/25:10511828 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rdr6Dojr1J" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rdr6Dojr1J</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2025.104174" target="_blank" >10.1016/j.ejc.2025.104174</a>

Result language
angličtina
Original language name
Sparsity of 3-flow-critical graphs
Original language description
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 K2 and K4 has at least 53 n 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. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Czech name
—
Czech description
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Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/LL2328" target="_blank" >LL2328: Beyond the Four Color Theorem</a>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP) I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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