Title:

A simple proof of Whitney's Theorem on connectivity in graphs (English) 
Author:

Zhao, Kewen 
Language:

English 
Journal:

Mathematica Bohemica 
ISSN:

08627959 
Volume:

136 
Issue:

1 
Year:

2011 
Pages:

2526 
Summary lang:

English 
. 
Category:

math 
. 
Summary:

In 1932 Whitney showed that a graph $G$ with order $n\geq 3$ is 2connected if and only if any two vertices of $G$ are connected by at least two internallydisjoint paths. The above result and its proof have been used in some Graph Theory books, such as in Bondy and Murty's wellknown Graph Theory with Applications. In this note we give a much simple proof of Whitney's Theorem. (English) 
Keyword:

connectivity 
Keyword:

graph 
MSC:

05C38 
MSC:

05C45 
idZBL:

Zbl 1224.05278 
idMR:

MR2807705 
. 
Date available:

20110331T11:20:42Z 
Last updated:

20130731 
Stable URL:

http://hdl.handle.net/10338.dmlcz/141446 
. 
Reference:

[1] Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications.Elsevier, New York (1976). MR 0411988 
Reference:

[2] Whitney, H.: Congruent graphs and the connectivity of graphs.Amer. J. Math. 54 (1932), 150168. Zbl 0003.32804, MR 1506881, 10.2307/2371086 
Reference:

[3] Whitney, H.: Nonseparable and planar graphs.Trans. Amer. Math. Soc. 34 (1932), 339362. Zbl 0004.13103, MR 1501641, 10.1090/S00029947193215016412 
. 