Cycles as edge intersection hypergraphs Article Swipe

PDF

Related Concepts

Hypergraph Combinatorics Intersection (aeronautics) Wedge (geometry) Mathematics Enhanced Data Rates for GSM Evolution Physics Geometry Computer science Geography Cartography Telecommunications

Martin Sonntag , Hanns‐Martin Teichert ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1902.00396 · OA: W2914311060

If ${\cal H}=(V,{\cal E})$ is a hypergraph, its edge intersection hypergraph $EI({\cal H})=(V,{\cal E}^{EI})$ has the edge set ${\cal E}^{EI}=\{e_1 \cap e_2 \ |\ e_1, e_2 \in {\cal E} \ \wedge \ e_1 \neq e_2 \ \wedge \ |e_1 \cap e_2 |\geq2\}$. 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 ${\cal H}=(V,{\cal E})$ with $\lceil \frac{n}{2} \rceil$ hyperedges and $EI({\cal H}) = C_n$.