On multiply critically h-connected graphs
β Scribed by Yahya Ould Hamidoune
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 262 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
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
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
## 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.
Mader conjectured that every non-complete \(k\)-critically \(n\)-connected graph has \((2 k+2)\) pairwise disjoint fragments. The conjecture was verified by Mader for \(k=1\). In this paper, we prove that this conjecture holds also for \(k=2\). 1993 Academic Press. Inc.