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Maximizing the Number of Independent Sets of a Fixed Size

Published online by Cambridge University Press:  14 October 2014

WENYING GAN ,
PO-SHEN LOH  and
BENNY SUDAKOV
WENYING GAN
Affiliation:
Department of Mathematics, ETH, 8092 Zurich, Switzerland (e-mail: ganw@math.ethz.ch, benjamin.sudakov@math.ethz.ch)
PO-SHEN LOH
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: ploh@cmu.edu)
BENNY SUDAKOV
Affiliation:
Department of Mathematics, ETH, 8092 Zurich, Switzerland (e-mail: ganw@math.ethz.ch, benjamin.sudakov@math.ethz.ch)
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Abstract

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.

Keywords

Primary 05C69Secondary 05D99
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Issue 3 , May 2015 , pp. 521 - 527
Copyright
Copyright © Cambridge University Press 2014 

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