Edge 4-critical Koester graph of order 28. Full article
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Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2023, Volume: 20, Number: 2, Pages: 847-853 Pages count : 7 DOI: 10.33048/semi.2023.20.051 | ||
| Tags | plane graph, 4-critical graph, Grotzsch-Sachs graph, Koester graph | ||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
A Koester graph G is a simple 4-regular plane graph formed by the superposition of a set S of circles in the plane, no two of which are tangent and no three circles have a common point. Crossing points and arcs of S correspond to vertices and edges of G, respectively. A graph G is edge critical if the removal of any edge decreases its chromatic number. A 4-chromatic edge critical Koester graph of order 28 generated by intersection of six circles is presented. This improves an upper bound for the smallest order of such graphs. The previous upper bound was established by Gerhard Koester in 1984 by constructing a graph with 40 vertices.
Cite:
Dobrynin A.A.
Edge 4-critical Koester graph of order 28.
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N2. P.847-853. DOI: 10.33048/semi.2023.20.051 WOS Scopus
Edge 4-critical Koester graph of order 28.
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N2. P.847-853. DOI: 10.33048/semi.2023.20.051 WOS Scopus
Dates:
| Submitted: | Jun 3, 2023 |
| Published print: | Oct 26, 2023 |
Identifiers:
| Web of science: | WOS:001095866000002 |
| Scopus: | 2-s2.0-85176574384 |
Citing:
| DB | Citing |
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| Web of science | 1 |