极大平面图的结构与着色理论(2)多米诺构形与扩缩运算

doi:10.11999/JEIT160224

CORC > 北京大学 > 信息科学技术学院

	极大平面图的结构与着色理论(2)多米诺构形与扩缩运算; Theory on Structure and Coloring of Maximal Planar Graphs (2) Domino Configurations and Extending-Contracting Operations
	许进
刊名	电子与信息学报
	2016
关键词	极大平面图扩缩运算多米诺构形祖先图子孙图递推构造法 Maximal planar graphs Extending-contracting operations Domino configurations Ancestor-graphs Descendent-graphs Recursive construction approach
DOI	10.11999/JEIT160224
英文摘要	业已证明四色猜想的数学证明可归结为刻画4-色漏斗型伪唯一4-色极大平面图的特征。为刻画此类极大平面图的结构特征，本文提出一种构造极大平面图的方法扩缩运算。研究发现：此方法的关键问题是需要清楚一种构形，称为多米诺构形。文中构造性地给出了多米诺构形的充要条件；在此基础上提出并建立了一个图的祖先图与子孙图理论与构造方法。特别证明了：任一最小度4的(9)n -阶极大平面图必含(2)n -阶或(3)n -阶祖先图；给出极大平面图的递推构造法，并用此方法构造出6~12-阶所有最小度4的极大平面图。扩缩运算是本系列文章的基石。; The first paper of this series of articles revealed that Four-Color Conjecture is hopefully proved mathematically by investigating a special class of graphs, called the 4-chromatic-funnel, pseudo uniquely-4-colorable maximal planar graphs. To characterize the properties of such class of graphs, a novel technique,“extending-contracting operation”, is proposed which can be used to construct maximal planar graphs. The essence of this technique is to study a special kind of configurations, domino configurations. In this paper, a necessary and sufficient condition for a planar graph to be a domino configuration is constructively given, on the basis of which it is proposed to construct the ancestor-graphs and descendent-graphs of a graph. Particularly, it is proved that every maximal planar graph with order ( 9)n and minimum degree 4 has an ancestor-graph of order ( 2)n or ( 3)n . Moreover, an approach is put forward to construct maximal planar graphs recursively, by which all maximal planar graphs with order 6~12 and minimum degree 4 are constructed. The extending-contracting operation constitutes the foundation in this series of articles.; 国家973规划项目; 国家自然科学基金(61372191,61472012,61472433,61572046,61502012,61572492,61572153,61402437)Foundation Items:The National 973 Program of China; The National Natural Science Foundation of China; EI; 中文核心期刊要目总览(PKU); 中国科技核心期刊(ISTIC); 中国科学引文数据库(CSCD); 6; 1271-1296; 38
语种	中文
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/493827]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	许进. 极大平面图的结构与着色理论(2)多米诺构形与扩缩运算, Theory on Structure and Coloring of Maximal Planar Graphs (2) Domino Configurations and Extending-Contracting Operations[J]. 电子与信息学报,2016.
APA	许进.(2016).极大平面图的结构与着色理论(2)多米诺构形与扩缩运算.电子与信息学报.
MLA	许进."极大平面图的结构与着色理论(2)多米诺构形与扩缩运算".电子与信息学报 (2016).