| Title:
|
A simple proof of Whitney's Theorem on connectivity in graphs (English) |
| Author:
|
Zhao, Kewen |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
25-26 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In 1932 Whitney showed that a graph $G$ with order $n\geq 3$ 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. (English) |
| Keyword:
|
connectivity |
| Keyword:
|
graph |
| MSC:
|
05C38 |
| MSC:
|
05C40 |
| MSC:
|
05C45 |
| idZBL:
|
Zbl 1224.05278 |
| idMR:
|
MR2807705 |
| DOI:
|
10.21136/MB.2011.141446 |
| . |
| Date available:
|
2011-03-31T11:20:42Z |
| Last updated:
|
2020-07-29 |
| 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), 150-168. Zbl 0003.32804, MR 1506881, 10.2307/2371086 |
| Reference:
|
[3] Whitney, H.: Non-separable and planar graphs.Trans. Amer. Math. Soc. 34 (1932), 339-362. Zbl 0004.13103, MR 1501641, 10.1090/S0002-9947-1932-1501641-2 |
| . |
