Lower bounds on the independence number in terms of the degrees
โ Scribed by Jerrold R Griggs
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 872 KB
- Volume
- 34
- 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
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.
## Abstract The number of independent vertex subsets is a graph parameter that is, apart from its purely mathematical importance, of interest in mathematical chemistry. In particular, the problem of maximizing or minimizing the number of independent vertex subsets within a given class of graphs has