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.
Characterization of maximum critically 2-connected graphs
✍ Scribed by R. C. Entringer
- Publisher
- John Wiley and Sons
- Year
- 1978
- Tongue
- English
- Weight
- 346 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
## Abstract In this paper we obtain chromatic polynomials __P(G__; λ) of 2‐connected graphs of order __n__ that are maximum for positive integer‐valued arguments λ ≧ 3. The extremal graphs are cycles __C__~__n__~ and these graphs are unique for every λ ≧ 3 and __n__ ≠ 5. We also determine max{__P(
## Abstract Let ${\cal{F}}\_{k}$ be the family of graphs __G__ such that all sufficiently large __k__ ‐connected claw‐free graphs which contain no induced copies of __G__ are subpancyclic. We show that for every __k__≥3 the family ${\cal{F}}\_{1}k$ is infinite and make the first step toward the c
## Abstract A graph __G__ = (__V__, __E__) is called weakly four‐connected if __G__ is 4‐edge‐connected and __G__ − __x__ is 2‐edge‐connected for all __x__ ∈ __V__. We give sufficient conditions for the existence of ‘splittable’ vertices of degree four in weakly four‐connected graphs. By using thes
Given a connected graph G, denote by V the family of all the spanning trees of G. Define an adjacency relation in V as follows: the spanning trees t and t$ are said to be adjacent if for some vertex u # V, t&u is connected and coincides with t$&u. The resultant graph G is called the leaf graph of G.
A graph G is radius-critical if every proper induced connected subgraph of G has radius strictly smaller than the original graph. Our main purpose is to characterize all such graphs. 1. By a graph we shall mean here a finite, simple, undirected graph. For a connected graph the distance between two