Every 3-polytope with minimum degree 5 has a 6-cycle with maximum degree at most 11

被引：6

作者：

Borodin, O. V. ^{[1
,2
]}

Ivanova, A. O. ^{[3
]}

Kostochka, A. V. ^{[1
,4
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Ammosov North Eastern Fed Univ, Yakutsk 677891, Russia

[4] Univ Illinois, Urbana, IL 61801 USA

来源：

DISCRETE MATHEMATICS | 2014年 / 315卷

基金：

俄罗斯基础研究基金会; 美国国家科学基金会;

关键词：

Planar graph; Plane map; Structure properties; 3-polytope; Weight; LIGHT SUBGRAPHS; PLANE GRAPHS; CYCLES;

D O I：

10.1016/j.disc.2013.10.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let phi(P)(C-6) (respectively, phi(T)(C-6)) be the minimum integer k with the property that every 3-polytope (respectively, every plane triangulation) with minimum degree 5 has a 6-cycle with all vertices of degree at most k. In 1999, S. Jendrol' and T. Madaras proved that 10 <= phi(T)(C-6) <= 11. It is also known, due to B. Mohar, R. Skrekovski and H.-J. Voss (2003), that phi(P)(C-6) <= 107. We prove that phi(P)(C-6) = phi(T)(C-6) = 11. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：128 / 134

页数：7