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arXiv · 1708.03785

Complete Subgraphs of the Coprime Hypergraph of Integers III: Construction

Jan-Hendrik de Wiljes
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Abstract

The coprime hypergraph of integers on $n$ vertices $CHI_k(n)$ is defined via vertex set $\{1,2,\dots,n\}$ and hyperedge set $\{\{v_1,v_2,\dots,v_{k+1}\}\subseteq\{1,2,\dots,n\}:\gcd(v_1,v_2,\dots,v_{k+1})=1\}$. In this article we present ideas on how to construct maximal subgraphs in $CHI_k(n)$. 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 give promising ideas for $k\geq 4$.

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Jan-Hendrik de Wiljes. 2017-08-12. Complete Subgraphs of the Coprime Hypergraph of Integers III: Construction. https://doi.org/10.1007/s40879-018-0254-9

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