Abstract
We continue to investigate structural properties of complete subgraphs of the coprime hypergraph of integers on n vertices 
, which has vertex set 
and hyperedge set 
. It turns out that any maximal complete subgraph G of 
has only vertices with at most three prime divisors for sufficiently large n. Further, we show that a vertex a of G with three prime divisors is squarefree and satisfies 
. We also give upper bounds for the number of prime divisors of vertices of G in case of arbitrary n.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
This operation has already been used, although not properly introduced, in [1].
References
de Wiljes, J.-H.: Complete subgraphs of the coprime hypergraph of integers I: introduction and bounds. Eur. J. Math. 3(2), 379–386 (2017)
Koshy, T.: Catalan Numbers with Applications. Oxford University Press, Oxford (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de Wiljes, JH. Complete subgraphs of the coprime hypergraph of integers II: structural properties. European Journal of Mathematics 4, 676–686 (2018). https://doi.org/10.1007/s40879-017-0176-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40879-017-0176-y