𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Connectivity keeping trees in k-connected graphs

✍ Scribed by W. Mader


Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
86 KB
Volume
69
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


We show that one can choose the minimum degree of a k-connected graph G large enough (independent of the vertex number of G) such that G contains a copy T of a prescribed tree with the property that G -V (T ) remains k-connected.


πŸ“œ SIMILAR VOLUMES


Connectivity keeping paths in k-connecte
✍ W. Mader πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 109 KB πŸ‘ 1 views

## Abstract A result of G. Chartrand, A. Kaugars, and D. R. Lick [Proc Amer Math Soc 32 (1972), 63–68] says that every finite, k‐connected graph __G__ of minimum degree at least ⌊3__k__/2βŒ‹ contains a vertex __x__ such that __G__βˆ’__x__ is still __k__‐connected. We generalize this result by proving t

On connectivities of tree graphs
✍ Guizhen Liu πŸ“‚ Article πŸ“… 1988 πŸ› John Wiley and Sons 🌐 English βš– 289 KB

Let T(G) be the tree graph of a graph G with cycle rank r. Then K ( T ( G ) ) 3 m ( G ) -r, where K(T(G)) and m(G) denote the connectivity of T ( G ) and the length of a minimum cycle basis for G, respectively. Moreover, the lower bound of m ( G ) -r is best possible.

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

Contractible subgraphs in k-connected gr
✍ Zemin Jin; Xingxing Yu; Xiaoyan Zhang πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 185 KB

## Abstract For a graph __G__ we define a graph __T__(__G__) whose vertices are the triangles in __G__ and two vertices of __T__(__G__) are adjacent if their corresponding triangles in __G__ share an edge. Kawarabayashi showed that if __G__ is a __k__‐connected graph and __T__(__G__) contains no ed

Nonseparating cycles in K-Connected grap
✍ Carsten Thomassen πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 192 KB πŸ‘ 1 views

## Abstract We show that every __k__‐connected graph with no 3‐cycle contains an edge whose contraction results in a __k__‐connected graph and use this to prove that every (__k__ + 3)‐connected graph contains a cycle whose deletion results in a __k__‐connected graph. This settles a problem of L. Lo