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.
A lower bound for the independence number of a planar graph
โ Scribed by Michael O Albertson
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 403 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We present a lower bound on the independence number of arbitrary hypergraphs in terms of the degree vectors. The degree vector of a vertex v is given by d is the number of edges of size m containing v. We define a function f with the property that any hypergraph H = (V, E) satisfies ฮฑ(H) โฅ vโV f (d
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