Lower bounds on the vulnerability of a graph
โ Scribed by F. T. Boesch
- Publisher
- John Wiley and Sons
- Year
- 1972
- Tongue
- English
- Weight
- 532 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Caro (1979) and Wei (1981) established a bound on the size of an independent set of a graph as a function of its degrees. In case the degrees of each vertex's neighbors are also known, we establish a lower bound which is tighter for most graphs.
The connectivity of a graph G and the corank of a matroid M are denoted by K(G) and p, respectively. X is shown that if a graph G is the base graph of a simple mat&d M, then K(G) L 2p and the lower bound of 2p izA best possible.
Lrzt G = (V, 0 be a ttlock :.>f order n, different from Kn. Let ~FI = min {d(x) + d(y): n then G contains a cycle of length at least m. 1. Introductlion and notatio e discuss only finite undirected graphs withsLc loops and multiple edges. We p:rosye the main theorem d show how Qre's th -orem [ 3.1 o