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Maximizing the Number of Independent Sets of a Fixed Size

  • WENYING GAN (a1), PO-SHEN LOH (a2) and BENNY SUDAKOV (a1)
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.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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