## Abstract Madar conjectured that every __k__‐critical __n__‐connected non‐complete graph __G__ has (2__k__ + 2) pairwise disjoint fragments. We show that Mader's conjecture holds if the order of __G__ is greater than (__k__ + 2)__n__. From this, it implies that two other conjectures on __k__‐crit
Fragments in 2-Critically n-Connected Graphs
✍ Scribed by J.J. Su
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 428 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0095-8956
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✦ Synopsis
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.
📜 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 À V ðH Þ is ðn À 3Þ-connected. This had been conjectured in Mader (High connectivity keeping sets in n-connected graphs, Combinatorica, to appear). Furthermore, we prove uppe
## Abstract A graph __G__ is critically 2‐connected if __G__ is 2‐connected but, for any point __p__ of __G, G — 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__ ⩾ 3, __n__ ≠ 11.
A graph G is N 2 -locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryja ´c ˇek conjectured that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. This conjecture is pro
## Abstract Mader conjectured that every __k__‐critical __n__‐connected noncomplete graph __G__ has __2k__ + 2 pairwise disjoint fragments. The author in 9 proved that the conjecture holds if the order of __G__ is greater than (__k__ + 2)__n__. Now we settle this conjecture completely. © 2004 Wiley