• DOI:10.7151/dmgt.2100
• Corpus ID: 119335965

On Selkow’s Bound on the Independence Number of Graphs

@article{Harant2019OnSB,
  title={On Selkow’s Bound on the Independence Number of Graphs},
  author={Jochen Harant and Samuel Mohr},
  journal={Discussiones Mathematicae Graph Theory},
  year={2019},
  volume={39},
  pages={655 - 657}
}

• J. Harant, Samuel Mohr
• Published 9 May 2017
• Mathematics
• Discussiones Mathematicae Graph Theory

Abstract For a graph G with vertex set V (G) and independence number α(G), Selkow [A Probabilistic lower bound on the independence number of graphs, Discrete Math. 132 (1994) 363–365] established the famous lower bound ∑v∈V(G)1d(v)+1(1+max{d(v)d(v)+1-∑u∈N(v)1d(u)+1,0}) $\sum {_{v \in V(G)}{1 \over {d(v) + 1}}} \left( {1 + \max \left\{ {{{d(v)} \over {d(v) + 1}} - \sum {_{u \in N(v)}{1 \over {d(u) + 1}},0} } \right\}} \right)$ on α (G), where N(v) and d(v) = |N(v)| denote the neighborhood and the degree of a vertex v ∈ V (G), respectively. However, Selkow’s original proof of this result is incorrect. We give a new probabilistic proof of Selkow’s bound here.