Реферат: Lebesgue (1940) proved that every plane graph with minimum degree δ at least 3 and girth g (the length of a shortest cycle) at least 5 has a path on three vertices (3-path) of degree 3 each. A description of 3-paths is tight if none of its parameter can be strengthened, and no triplet dropped. Borodin et al. (2013) gave a tight description of 3-paths in plane graphs with δ≥3 and g≥3, and another tight description was given by Borodin, Ivanova and Kostochka in 2017. In 2015, we gave seven tight descriptions of 3-paths when δ≥3 and g≥4. Furthermore, we proved that this set of tight descriptions is complete, which was a result of a new type in the structural theory of plane graphs. Also, we characterized (2018) all one-term tight descriptions if δ≥3 and g≥3. The problem of producing all tight descriptions for g≥3 remains widely open even for δ≥3. Eleven tight descriptions of 3-paths were obtained for plane graphs with δ=2 and g≥4 by Jendrol’, Maceková, Montassier, and Soták, four of which are descriptions for g≥9. In 2018, Aksenov, Borodin and Ivanova proved nine new tight descriptions of 3-paths for δ=2 and g≥9 and showed that no other tight descriptions exist. Recently, we resolved the case g≥8. The purpose of this paper is to give a complete list of 15 tight descriptions of 3-paths in the plane graphs with δ=2 and g≥7. © 2021 Elsevier B.V.

Библиографическая ссылка: Borodin O.V. , Ivanova A.O.
All tight descriptions of 3-paths in plane graphs with girth at least 7
Discrete Mathematics. 2021. V.344. N5. 112335 . DOI: 10.1016/j.disc.2021.112335 WOS Scopus OpenAlex

Идентификаторы БД:

Web of science:	WOS:000633365200007
Scopus:	2-s2.0-85101350799
OpenAlex:	W3129472824

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БД	Цитирований
Scopus	1
Web of science	1
OpenAlex	3

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