Light C4 and C5 in 3-polytopes with minimum degree 5

被引：5

作者：

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

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

Woodall, D. R. ^{[4
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Ammosov North Eastern Univ, Yakutsk 677013, Russia

[4] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

DISCRETE MATHEMATICS | 2014年 / 334卷

基金：

俄罗斯基础研究基金会;

关键词：

Planar graph; Plane map; Structure properties; 3-polytope; Weight; NORMAL PLANE MAPS; GRAPHS; SUBGRAPHS;

D O I：

10.1016/j.disc.2014.06.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let w(P)(C-1) (w(T)(C-1)) be the minimum integer k with the property that every 3-polytope (respectively, every plane triangulation) with minimum degree 5 has an l-cycle with weight, defined as the degree-sum of all vertices, at most k. In 1998, O.V. Borodin and DR. Woodall proved w(T)(C-4) = 25 and w(T)(C-5) = 30. We prove that w(P)(C-4) = 26 and w(P) (C-5) = 30. (C) 2014 Elsevier BM. All rights reserved.

引用

页码：63 / 69

页数：7

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