On Some Properties of Critically h-Connected Graphs and K-Critically h-Connected Graphs
β Scribed by JIANJI SU
- Book ID
- 119862802
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 315 KB
- Volume
- 576
- Category
- Article
- ISSN
- 0890-6564
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Su, J., On locally k-critically n-connected graphs, Discrete Mathematics 120 (1993) 183-190. Let 0 # W'g V(G). The graph G is called a W-locally k-critically n-connected graph or simply a W-locally (n, k)-graph, if for all V'G W with 1 V'I 6 k and each fragment F of G we have that K(G-V')=n-1 V' and
We prove that every n-connected graph G of sufficiently large order contains a connected graph H on four vertices such that G Γ V Γ°H Γ is Γ°n Γ 3Γ-connected. This had been conjectured in Mader (High connectivity keeping sets in n-connected graphs, Combinatorica, to appear). Furthermore, we prove uppe
## Abstract A graph __G__ is critically 2βconnected if __G__ is 2βconnected but, for any point __p__ of __G, G β p__ is not 2βconnected. Critically 2βconnected graphs on __n__ points that have the maximum number of lines are characterized and shown to be unique for __n__ β©Ύ 3, __n__ β 11.
A graph G which iit n-connected (but not (I! I)-connected) is defined ro be k-xitical if for every S 6; V(G), where f S i d k. the connectivity of G -I S is h -/S ia We will say that G is an (n\*,k\*) graph if G is n-conneckxt (b:lt nat (n t Itconnected) and k-crirical (hut not (k c l)criticaf). Thi