An analogue of Franklin's Theorem

被引：16

作者：

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

Ivanova, A. O. ^{[2
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Ammosov North Eastern Fed Univ, Yakutsk 677000, Russia

来源：

DISCRETE MATHEMATICS | 2016年 / 339卷 / 10期

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; LIGHT SUBGRAPHS; GRAPHS; 3-PATHS; VERTICES; GIRTH; PATHS;

D O I：

10.1016/j.disc.2016.04.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Back in 1922, Franklin proved that every 3-polytope P-5 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. The purpose of this note is to prove that every P-5 has a vertex of degree at most 6 adjacent to a 5-vertex and another vertex of degree at most 6, which is also tight. Moreover, we prove that there is no tight description of 3-paths in P(5)s other than these two. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：2553 / 2556

页数：4

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