New lower bounds for the independence number of sparse graphs and hypergraphs
Combinatorics
2011-02-25 v1
Abstract
We obtain new lower bounds for the independence number of -free graphs and linear -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.
Keywords
Cite
@article{arxiv.1102.4856,
title = {New lower bounds for the independence number of sparse graphs and hypergraphs},
author = {Kunal Dutta and Dhruv Mubayi and C. R. Subramanian},
journal= {arXiv preprint arXiv:1102.4856},
year = {2011}
}