A SIMPLE PROOF OF WHITNEY'S THEOREM ON CONNECTIVITY IN GRAPHS

被引：0

作者：

Zhao, Kewen ^{[1
]}

机构：

[1] Moorhead State Univ, Dept Comp Sci & Informat Syst, Moorhead, MN 56563 USA

来源：

MATHEMATICA BOHEMICA | 2011年 / 136卷 / 01期

关键词：

connectivity; graph;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1932 Whitney showed that a graph G with order n >= 3 is 2-connected if and only if any two vertices of G are connected by at least two internally -disjoint paths. The above result and its proof have been used in some Graph Theory books, such as in Bondy and Murty's well-known Graph Theory with Applications. In this note we give a much simple proof of Whitney's Theorem.

引用

页码：25 / 37

页数：14

共 50 条

[11] Short proof of Menger's Theorem [J].

Göring, F .

DISCRETE MATHEMATICS, 2000, 219 (1-3) :295-296

[12] A New Proof of Bartholdi's Theorem [J].

Hirobumi Mizuno ;

Iwao Sato .

Journal of Algebraic Combinatorics, 2005, 22 :259-271

[13] A new proof of Bartholdi's theorem [J].

Mizuno, H ;

Sato, I .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2005, 22 (03) :259-271

[14] A connectivity game for graphs [J].

Rafael Amer ;

José Miguel Giménez .

Mathematical Methods of Operations Research, 2004, 60 :453-470

[15] A connectivity game for graphs [J].

Amer, R ;

Giménez, JM .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2004, 60 (03) :453-470

[16] Structure connectivity and substructure connectivity of star graphs [J].

Li, Chunfang ;

Lin, Shangwei ;

Li, Shengjia .

DISCRETE APPLIED MATHEMATICS, 2020, 284 :472-480

[17] Eulerian Subgraphs and S-connectivity of Graphs [J].

Han, Miaomiao ;

Miao, Zhengke .

APPLIED MATHEMATICS AND COMPUTATION, 2020, 382

[18] Mader's conjecture for graphs with small connectivity [J].

Hong, Yanmei ;

Liu, Qinghai .

JOURNAL OF GRAPH THEORY, 2022, 101 (03) :379-388

[19] HAJóS' CONJECTURE AND CONNECTIVITY OF EULERIAN GRAPHS [J].

XU Baogang (School of Mathematics and Computer Science .

Journal of Systems Science & Complexity, 2002, (03) :295-298

[20] Proof of a conjecture on connectivity keeping odd paths in k-connected bipartite graphs ☆ [J].

Yang, Qing ;

Tian, Yingzhi .

DISCRETE MATHEMATICS, 2025, 348 (08)

← 1 2 3 4 5 →