The main aim of the present note is the proof of a variant of the MENGER-WHITNEY theorem on n-connected graphs (Theorem 1 below). While the result itself is well known (being, for example, a special case of the theorem of MENGER mentioned in Remark I), two of its aspects deserve attention. First, it
Hamilto-connected derangement graphs on S n
β Scribed by David J. Rasmussen; Carla D. Savage
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 476 KB
- Volume
- 133
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A graph G is (n, \*)-connected if it satisfies the following conditions: (1) |V(G)| n+1; (2) for any subset S V(G) and any subset L E(G) with \* |S| +|L| <n\*, G&S&L is connected. The (n, \*)-connectivity is a common extension of both the vertex-connectivity and the edge-connectivity. An (n, 1)-conn
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
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 Mader conjectured that every __k__βcritical __n__βconnected noncomplete graph __G__ has __2k__β+β2 pairwise disjoint fragments. The author in 9 proved that the conjecture holds if the order of __G__ is greater than (__k__β+β2)__n__. Now we settle this conjecture completely. Β© 2004 Wiley