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On critically h-connected simple graphs

✍ Scribed by Yaha Ould Hamidoune


Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
227 KB
Volume
32
Category
Article
ISSN
0012-365X

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✍ W. Mader πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 221 KB

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 Þ is Γ°n Γ€ 3Þ-connected. This had been conjectured in Mader (High connectivity keeping sets in n-connected graphs, Combinatorica, to appear). Furthermore, we prove uppe

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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

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✍ Kiyoshi Ando; Yoko Usami πŸ“‚ Article πŸ“… 1987 πŸ› Elsevier Science 🌐 English βš– 359 KB
Characterization of maximum critically 2
✍ R. C. Entringer πŸ“‚ Article πŸ“… 1978 πŸ› John Wiley and Sons 🌐 English βš– 346 KB

## Abstract A graph __G__ is critically 2‐connected if __G__ is 2‐connected but, for any point __p__ of __G, G β€” p__ is not 2‐connected. Critically 2‐connected 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.

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✍ J.J. Su πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 428 KB

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.