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Critically (k, k)-connected graphs

✍ Scribed by Kiyoshi Ando; Yoko Usami


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
359 KB
Volume
66
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


On k-con-Critically n-Connected Graphs
✍ 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

On locally k-critically n-connected grap
✍ Jianji Su πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 479 KB

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

On k-critical, n-connected graphs
✍ Stephen Maurer; Peter J. Slater πŸ“‚ Article πŸ“… 1977 πŸ› Elsevier Science 🌐 English βš– 718 KB

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

k-shredders in k-connected graphs
✍ Yoshimi Egawa πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 184 KB πŸ‘ 1 views

## Abstract For a graph __G__, a subset __S__ of __V__(__G__) is called a shredder if __G__β€‰βˆ’β€‰__S__ consists of three or more components. We show that if __k__ β‰₯ 4 and __G__ is a __k__‐connected graph, then the number of shredders of cardinality __k__ of __G__ is less than 2|__V__(__G__)|/3 (we sho

Minimally (k, k)-edge-connected graphs
✍ Kamal Hennayake; Hong-Jian Lai; Deying Li; Jingzhong Mao πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 138 KB πŸ‘ 1 views

## Abstract For an integer __l__ > 1, the __l__‐edge‐connectivity of a connected graph with at least __l__ vertices is the smallest number of edges whose removal results in a graph with __l__ components. A connected graph __G__ is (__k__, __l__)‐edge‐connected if the __l__‐edge‐connectivity of __G_

The k-Critical 2k-Connected Graphs for k
✍ Matthias Kriesell πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 180 KB

A noncomplete graph G is called an (n, k)-graph if it is n-connected and G&X is not (n&|X | +1)-connected for any X V(G) with |X | k. Mader conjectured that for k 3 the graph K 2k+2 -(1-factor) is the unique (2k, k)-graph. We settle this conjecture for k 4.