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
收藏
页码:25 / 37
页数:14
相关论文
共 50 条
[21]   A short proof of the versatile version of Fleischner's theorem [J].
Muettel, Janina ;
Rautenbach, Dieter .
DISCRETE MATHEMATICS, 2013, 313 (19) :1929-1933
[22]   An inductive proof of Dirac's theorem on Hamilton cycles☆ [J].
Ning, Bo .
DISCRETE APPLIED MATHEMATICS, 2025, 365 :160-162
[23]   Star complements and connectivity in finite graphs [J].
Rowlinson, Peter .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 442 :92-98
[24]   On the connectivity properties and energy of Fibonomial graphs [J].
Akbulak, Mehmet ;
Kale, Akin ;
Oteles, Ahmet .
DISCRETE APPLIED MATHEMATICS, 2014, 169 :1-8
[25]   A CONCEPT OF WEIGHTED CONNECTIVITY ON CONNECTED GRAPHS [J].
Amer, Rafael ;
Gimenez, Jose Miguel .
APLIMAT 2009: 8TH INTERNATIONAL CONFERENCE, PROCEEDINGS, 2009, :43-48
[26]   PROOF OF SLATER'S CONJECTURE ON k-CRITICAL n-CONNECTED GRAPHS [J].
苏健基 .
Science Bulletin, 1988, (20) :1675-1678
[27]   AN ALTERNATE PROOF OF WISE'S MALNORMAL SPECIAL QUOTIENT THEOREM [J].
Agol, Ian ;
Groves, Daniel ;
Manning, Jason Fox .
FORUM OF MATHEMATICS PI, 2016, 4 :1-54
[28]   On local connectivity of graphs [J].
Volkmann, Lutz .
APPLIED MATHEMATICS LETTERS, 2008, 21 (01) :63-66
[29]   On the Connectivity of Visibility Graphs [J].
Payne, Michael S. ;
Por, Attila ;
Valtr, Pavel ;
Wood, David R. .
DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 48 (03) :669-681
[30]   The Connectivity of Token Graphs [J].
J. Leaños ;
A. L. Trujillo-Negrete .
Graphs and Combinatorics, 2018, 34 :777-790