A simple proof of Whitney's Theorem on connectivity in graphs
Mathematica Bohemica (2011)
- Volume: 136, Issue: 1, page 25-26
- ISSN: 0862-7959
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Abstract
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topZhao, Kewen. "A simple proof of Whitney's Theorem on connectivity in graphs." Mathematica Bohemica 136.1 (2011): 25-26. <http://eudml.org/doc/196590>.
@article{Zhao2011,
abstract = {In 1932 Whitney showed that a graph $G$ with order $n\ge 3$ 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.},
author = {Zhao, Kewen},
journal = {Mathematica Bohemica},
keywords = {connectivity; graph; connectivity; graph},
language = {eng},
number = {1},
pages = {25-26},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A simple proof of Whitney's Theorem on connectivity in graphs},
url = {http://eudml.org/doc/196590},
volume = {136},
year = {2011},
}
TY - JOUR
AU - Zhao, Kewen
TI - A simple proof of Whitney's Theorem on connectivity in graphs
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 1
SP - 25
EP - 26
AB - In 1932 Whitney showed that a graph $G$ with order $n\ge 3$ 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.
LA - eng
KW - connectivity; graph; connectivity; graph
UR - http://eudml.org/doc/196590
ER -
References
top- Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, Elsevier, New York (1976). (1976) MR0411988
- Whitney, H., 10.2307/2371086, Amer. J. Math. 54 (1932), 150-168. (1932) Zbl0003.32804MR1506881DOI10.2307/2371086
- Whitney, H., 10.1090/S0002-9947-1932-1501641-2, Trans. Amer. Math. Soc. 34 (1932), 339-362. (1932) Zbl0004.13103MR1501641DOI10.1090/S0002-9947-1932-1501641-2
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