Реферат: The height of a face in a 3-polytope is the maximum degree of the incident vertices of the face, and the height of a 3-polytope, h, is the minimum height of its faces. A face is pyramidal if it is either a 4-face incident with three 3-vertices, or a 3-face incident with two vertices of degree at most 4. If pyramidal faces are allowed, then h can be arbitrarily large; so we assume the absence of pyramidal faces. In 1940, Lebesgue proved that every quadrangulated 3-polytope has h ≤ 11. In 1995, this bound was lowered by Avgustinovich and Borodin to 10. Recently, we improved it to the sharp bound 8. For plane triangulation without 4-vertices, Borodin (1992), confirming the Kotzig conjecture of 1979, proved that h ≤ 20 which bound is sharp. Later, Borodin (1998) proved that h ≤ 20 for all triangulated 3-polytopes. Recently, we obtained the sharp bound 10 for triangle-free 3-polytopes. In 1996, Horňák and Jendrol’ proved for arbitrarily 3-polytopes that h ≤ 23. In this paper we improve this bound to the sharp bound 20. © 2017, Pleiades Publishing, Ltd.

Библиографическая ссылка: Borodin O.V. , Ivanova A.O.
The height of faces of 3-polytopes
Siberian Mathematical Journal. 2017. V.58. N1. P.37-42. DOI: 10.1134/S0037446617010050 WOS Scopus OpenAlex

Идентификаторы БД:

Web of science:	WOS:000396065100005
Scopus:	2-s2.0-85014722960
OpenAlex:	W2593361153

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БД	Цитирований
Scopus	4
OpenAlex	4
Web of science	3

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