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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 5, Pages 981–987
DOI: https://doi.org/10.17377/smzh.2016.57.504 (Mi smj2799) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Describing $4$-paths in $3$-polytopes with minimum degree $5$

O. V. Borodina, A. O. Ivanovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Ammosov North-Eastern Federal University, Yakutsk, Russia
Full-text PDF (553 kB) Citations (6)
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DOI: https://doi.org/10.17377/smzh.2016.57.504
Abstract: Back in 1922, Franklin proved that each $3$-polytope with minimum degree $5$ has a $5$-vertex adjacent to two vertices of degree at most $6$, which is tight. This result has been extended and refined in several directions. In particular, Jendrol' and Madaras (1996) ensured a $4$-path with the degree-sum at most $23$. The purpose of this note is to prove that each 3-polytope with minimum degree $5$ has a $(6,5,6,6)$-path or $(5,5,5,7)$-path, which is tight and refines both above mentioned results.
Keywords: planar graph, plane map, structure properties, $3$-polytope, $4$-path.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00499
15-01-05867
The first author was supported by the Russian Foundation for Basic Research (Grants 15-01-05867 and 16-01-00499) and the second author worked within the governmental task “Organization of Scientific Research”.
Received: 23.11.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 5, Pages 764–768
DOI: https://doi.org/10.1134/S0037446616050049
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: O. V. Borodin, A. O. Ivanova, “Describing $4$-paths in $3$-polytopes with minimum degree $5$”, Sibirsk. Mat. Zh., 57:5 (2016), 981–987; Siberian Math. J., 57:5 (2016), 764–768
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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