Email this article Describing 4-paths in 3-polytopes with minimum degree 5
- Authors: Borodin O.V.1, Ivanova A.O.2
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Affiliations:
- Sobolev Institute of Mathematics
- Ammosov North-Eastern Federal University
- Issue: Vol 57, No 5 (2016)
- Pages: 764-768
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170674
- DOI: https://doi.org/10.1134/S0037446616050049
- ID: 170674
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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.
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About the authors
O. V. Borodin
Sobolev Institute of Mathematics
Author for correspondence.
Email: brdnoleg@math.nsc.ru
Russian Federation, Novosibirsk
A. O. Ivanova
Ammosov North-Eastern Federal University
Email: brdnoleg@math.nsc.ru
Russian Federation, Yakutsk
