Cliques in graphs excluding a complete graph minor

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This paper considers the following question: What is the maximum number of k-cliques in an n-vertex graph with no Kt-minor? This question generalises the extremal function for Kt-minors, which corresponds to the k = 2 case. The exact answer is given for t ≤ 9 and all values of k. We also determine the maximum total number of cliques in an n-vertex graph with no Kt-minor for t ≤ 9. Several observations are made about the case of general t.

Original languageEnglish
Article numberP3.18
Number of pages16
JournalElectronic Journal of Combinatorics
Issue number3
Publication statusPublished - 5 Aug 2016


  • Clique
  • Graph theory
  • Minor

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