Cycles as edge intersection hypergraphs

Abstract

If $\mathcal{H}=(V,\mathcal{E})$ is a hypergraph, its edge intersection hypergraph $EI(\mathcal{H})=(V,{\mathcal{E}}^{EI})$ has the edge set ${\mathcal{E}}^{EI}=\{e_1\cap e_2|e_1,e_2\in \mathcal{E}\wedge e_1\ne e_2\wedge |e_1\cap e_2|\ge 2\}$. Picking up a problem from arXiv:1901.06292, for $n\ge 24$ we prove that there is a 3-regular (and - if $n$ is even - 6-uniform) hypergraph $\mathcal{H}=(V,\mathcal{E})$ with $\lceil \frac{n}{2}\rceil$ hyperedges and $EI(\mathcal{H})=C_n$.

arXiv comment21 pages

References in corpus (2)

• Edge Intersection Graphs of L-Shaped Paths in Grids
• Edge intersection hypergraphs - a new hypergraph concept