Complete subgraphs of the coprime hypergraph of integers III: construction

Abstract

The coprime hypergraph of integers on n vertices is defined via vertex set \(\{1,2,\dots ,n\}\) and hyperedge set . We present ideas on how to construct maximal complete subgraphs in . This continues the author’s earlier work, which dealt with bounds on the size and structural properties of these subgraphs. We succeed in the cases \(k\in \{1,2,3\}\) and discuss promising ideas for \(k\geqslant 4\).

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Fig. 1

Notes

  1. 1.

    We could also view it as a set of size and label the vertices accordingly. Our way avoids the need to distinguish between vertex and label, which could lead to confusion.

  2. 2.

    The precision of the terms “close” has to be determined.

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    de Wiljes, J.-H.: Complete subgraphs of the coprime hypergraph of integers II: structural properties. Eur. J. Math. 4(2), 676–686 (2018)

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Correspondence to Jan-Hendrik de Wiljes.

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de Wiljes, JH. Complete subgraphs of the coprime hypergraph of integers III: construction. European Journal of Mathematics 5, 1396–1403 (2019). https://doi.org/10.1007/s40879-018-0254-9

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Keywords

  • Hypergraph on integers
  • Clique
  • Matching

Mathematics Subject Classification

  • 11B75
  • 05C65
  • 05C69
  • 05C70