New lower bounds for the independence number of sparse graphs and hypergraphs

Details New lower bounds for the independence number of sparse graphs and hypergraphs New lower bounds for the independence number of sparse graphs and hypergraphs

2011-02-23

arxiv.org/abs/1102.4856v1

Mathematics

Combinatorics

Scientific paper

We obtain new lower bounds for the independence number of $K_r$-free graphs and linear $k$-uniform hypergraphs in terms of the degree sequence. This answers some old questions raised by Caro and Tuza \cite{CT91}. Our proof technique is an extension of a method of Caro and Wei \cite{CA79, WE79}, and we also give a new short proof of the main result of \cite{CT91} using this approach. As byproducts, we also obtain some non-trivial identities involving binomial coefficients.

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