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European Journal of Mathematics

, Volume 3, Issue 2, pp 379–386 | Cite as

Complete subgraphs of the coprime hypergraph of integers I: introduction and bounds

  • Jan-Hendrik de WiljesEmail author
Research Article

Abstract

We introduce the uniform coprime hypergraph of integers \(\mathrm{CHI}_k\) which is the graph with vertex set \({\mathbb {Z}}\) and a Open image in new window -hyperedge exactly between every \(k+1\) elements of \({\mathbb {Z}}\) having greatest common divisor equal to 1. This generalizes the concept of coprime graphs. We obtain some basic properties of these graphs and give upper and lower bounds for the clique number of certain subgraphs of \(\mathrm{CHI}_k\).

Keywords

Hypergraphs on integers Clique number Degree sequence 

Mathematics Subject Classification

11B75 05C65 05C69 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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