A new 4-chromatic edge critical Koester graph Full article
Journal |
Discrete Mathematics Letters
ISSN: 2664-2557 |
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Output data | Year: 2023, Volume: 12, Pages: 6-10 Pages count : 5 DOI: 10.47443/dml.2022.166 | ||
Tags | plane graph; 4-critical graph; Gro¨tzsch–Sachs graph; Koester graph | ||
Authors |
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Affiliations |
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Funding (1)
1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
Let S be a decomposition of a simple 4-regular plane graph into edge-disjoint cycles such that every two adjacent edges on a face belong to different cycles of S. Such graphs, called Gr¨ otzsch–Sachs graphs, may be considered as a result of a superposition of simple closed curves in the plane with tangencies disallowed. Koester studied the coloring of Gr¨otzschSachs graphs when all curves are circles. In 1984, he presented the first example of a 4-chromatic edge critical plane graph of order 40 formed by 7 circles. In the present paper, a new 4-chromatic edge critical graph generated by circles in the plane is presented.
Cite:
Dobrynin A.A.
A new 4-chromatic edge critical Koester graph
Discrete Mathematics Letters. 2023. V.12. P.6-10. DOI: 10.47443/dml.2022.166 WOS Scopus OpenAlex
A new 4-chromatic edge critical Koester graph
Discrete Mathematics Letters. 2023. V.12. P.6-10. DOI: 10.47443/dml.2022.166 WOS Scopus OpenAlex
Dates:
Submitted: | Jan 25, 2023 |
Accepted: | Feb 13, 2023 |
Published print: | Mar 7, 2023 |
Published online: | Mar 7, 2023 |
Identifiers:
Web of science: | WOS:001065538700002 |
Scopus: | 2-s2.0-85176583730 |
OpenAlex: | W4323352235 |