@article{HM19selkow,
title={On Selkowâ€™s bound on the independence number of graphs},
author={Harant, Jochen and Mohr, Samuel},
journal={Discussiones Mathematicae Graph Theory},
volume={39},
number={3},
pages={655--657},
year={2019},
publisher={Sciendo},
doi = {10.7151/dmgt.2100},
archivePrefix = {arXiv},
eprint = {1705.03779},
biburl = {http://samuel-mohr.de/files/bib/2.bib},
abstract = {For a graph {$G$} with vertex set {$V(G)$} and independence number {$\alpha(G)$}, S.~M.~Selkow (Discrete Mathematics, 132(1994)363--365) established the famous lower bound {$\sum\limits_{v\in V(G)}\frac{1}{d(v)+1}(1+\max\{\frac{d(v)}{d(v)+1}-\sum\limits_{u\in N(v)}\frac{1}{d(u)+1},0 \})$} on {$\alpha(G)$}, where {$N(v)$} and {$d(v)=|N(v)|$} denote the neighborhood and the degree of a vertex {$v\in V(G)$}, respectively. However, Selkow's original proof of this result is incorrect. We give a new probabilistic proof of Selkow's bound here.
}
}