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.
β¦ LIBER β¦
A new lower bound on the independence number of graphs
β Scribed by Angel, Eric; Campigotto, Romain; Laforest, Christian
- Book ID
- 122079920
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 228 KB
- Volume
- 161
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
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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 Ξ±(H) β₯ vβV f (d