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 on the independence number of a graph
โ Scribed by Jochen Harant
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 210 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
A new lower bound on the independence number of a graph is established and an accompanying efficient algorithm constructing an independent vertex set the cardinality of which is at least this lower bound is given. (~
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
Let \_(n, m, k) be the largest number \_ # [0, 1] such that any graph on n vertices with independence number at most m has a subgraph on k vertices with at lest \_ } ( k 2 ) edges. Up to a constant multiplicative factor, we determine \_(n, m, k) for all n, m, k. For log n m=k n, our result gives \_(