The numbers of dependent k-sets in a graph are log concave

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Abstract

A set of vertices in a graph is said to be dependent if it is not independent. Let pk(G) denote the number of dependent sets of size k in the graph G. We show that, for any graph G, the sequence {pk(G)} is logarithmically concave. © 2001 Elsevier Science.

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Horrocks, D. G. C. (2002). The numbers of dependent k-sets in a graph are log concave. Journal of Combinatorial Theory. Series B, 84(1), 180–185. https://doi.org/10.1006/jctb.2001.2077

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