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

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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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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    O. V. Borodin

  2. Ammosov North-Eastern Federal University, Yakutsk, Russia

    A. O. Ivanova

Authors
  1. O. V. Borodin
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  2. A. O. Ivanova
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Corresponding author

Correspondence to O. V. Borodin.

Additional information

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.”

Novosibirsk; Yakutsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 981–987, September–October, 2016; DOI: 10.17377/smzh.2016.57.504.

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Borodin, O.V., Ivanova, A.O. Describing 4-paths in 3-polytopes with minimum degree 5. Sib Math J 57, 764–768 (2016). https://doi.org/10.1134/S0037446616050049

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  • DOI: https://doi.org/10.1134/S0037446616050049

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