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Complete subgraphs of the coprime hypergraph of integers III: construction

  • Jan-Hendrik de WiljesEmail author
Research Article

Abstract

The coprime hypergraph of integers on n vertices Open image in new window is defined via vertex set \(\{1,2,\dots ,n\}\) and hyperedge set Open image in new window . We present ideas on how to construct maximal complete subgraphs in Open image in new window . 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 \(k\geqslant 4\).

Keywords

Hypergraph on integers Clique Matching 

Mathematics Subject Classification

11B75 05C65 05C69 05C70 

References

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    Berge, C.: Two theorems in graph theory. Proc. Nat. Acad. Sci. USA 43(9), 842–844 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
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    Bondy, J.A., Murty, U.S.R.: Graph Theory. Graduate Texts in Mathematics, vol. 244. Springer, New York (2008)zbMATHGoogle Scholar
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    de Wiljes, J.-H.: Complete subgraphs of the coprime hypergraph of integers I: introduction and bounds. Eur. J. Math. 3(2), 379–386 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
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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)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics and Applied Computer ScienceUniversity of HildesheimHildesheimGermany

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