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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Notes
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.The precision of the terms “close” has to be determined.
and label the vertices accordingly. Our way avoids the need to distinguish between vertex and label, which could lead to confusion.References
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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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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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DOI: https://doi.org/10.1007/s40879-018-0254-9