Date of Original Version

1-2014

Type

Article

Rights Management

© Cambridge University Press

Abstract or Description

Let it (G) be the number of independent sets of size t in a graph G. Engbers and Galvin asked how large it (G) could be in graphs with minimum degree at least δ. They further conjectured that when n ≥ 2δ and t ≥ 3, it (G) is maximized by the complete bipartite graph Kδ,n−δ . This conjecture has recently drawn the attention of many researchers. In this short note, we prove this conjecture.

DOI

10.1017/S0963548314000546

Included in

Mathematics Commons

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Published In

Combinatorics, Probability and Computing, 24, 3, 521-527.