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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2006, Volume 3, Pages 428–440
(Mi semr218)
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This article is cited in 12 scientific papers (total in 12 papers)
Research papers
Planar graphs without triangles adjacent to cycles of length from $3$ to $9$ are $3$-colorable
O. V. Borodina, A. N. Glebova, T. R. Jensenb, A. Raspaudc a Institute of Mathematics, Novosibirsk, Russia
b Alpen-Adria Universität Klagenfurt, Institut für Mathematik, Austria
c Université Bordeaux I, France
Abstract:
Planar graphs without triangles adjacent to cycles of length from $3$ to $9$ are proved to be $3$-colorable, which extends Grötzsch's theorem. We conjecture that planar graphs without $3$-cycles adjacent to cycles of length $3$ or $5$ are $3$-colorable.
Received December 14, 2006, published December 23, 2006
Citation:
O. V. Borodin, A. N. Glebov, T. R. Jensen, A. Raspaud, “Planar graphs without triangles adjacent to cycles of length from $3$ to $9$ are $3$-colorable”, Sib. Èlektron. Mat. Izv., 3 (2006), 428–440
Linking options:
https://www.mathnet.ru/eng/semr218 https://www.mathnet.ru/eng/semr/v3/p428
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Abstract page: | 632 | Full-text PDF : | 108 | References: | 67 |
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