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] A New Proof of Bartholdi's Theorem
Hirobumi Mizuno
Iwao Sato
Journal of Algebraic Combinatorics, 2005, 22 : 259 - 271
[12] A new proof of Bartholdi's theorem
Mizuno, H
Sato, I
JOURNAL OF ALGEBRAIC COMBINATORICS, 2005, 22 (03) : 259 - 271
[13] Short proof of Menger's Theorem
Göring, F
DISCRETE MATHEMATICS, 2000, 219 (1-3) : 295 - 296
[14] A connectivity game for graphs
Rafael Amer
José Miguel Giménez
Mathematical Methods of Operations Research, 2004, 60 : 453 - 470
[15] A connectivity game for graphs
Amer, R
Giménez, JM
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2004, 60 (03) : 453 - 470
[16] Structure connectivity and substructure connectivity of star graphs
Li, Chunfang
Lin, Shangwei
Li, Shengjia
DISCRETE APPLIED MATHEMATICS, 2020, 284 : 472 - 480
[17] Eulerian Subgraphs and S-connectivity of Graphs
Han, Miaomiao
Miao, Zhengke
APPLIED MATHEMATICS AND COMPUTATION, 2020, 382 (382)
[18] HAJóS' CONJECTURE AND CONNECTIVITY OF EULERIAN GRAPHS
XU Baogang (School of Mathematics and Computer Science
Journal of Systems Science & Complexity, 2002, (03) : 295 - 298
[19] Mader's conjecture for graphs with small connectivity
Hong, Yanmei
Liu, Qinghai
JOURNAL OF GRAPH THEORY, 2022, 101 (03) : 379 - 388
[20] A short proof of the versatile version of Fleischner's theorem
Muettel, Janina
Rautenbach, Dieter
DISCRETE MATHEMATICS, 2013, 313 (19) : 1929 - 1933

← 1 2 3 4 5 →