Cycles as edge intersection hypergraphs of $k$-uniform hypergraphs ($k \le 6$) -- a constructive approach
Year: 2022
Type: preprint
Abstract: If ${\cal H}=(V,{\cal E})$ is a hypergraph, its edge intersection hypergraph $EI({\cal H})=(V,{\cal E}^{EI})$ has the edge set ${\cal E}^{EI}=\{e_1 \cap e_2 \ |\ e_1, e_2 \in {\cal E} \ \wedge \ e_1 \neq e_2 \ \wedge \ |e_1 \cap e_2 |\geq 2\}$. In the present paper, we consider 4- and 5-uniform hypergraphs ${\cal H}$, respectively, with $EI({\cal H}) = C_n$. Our results fill the gap between the 3- and the 6-uniform case considered in arXiv:1902.00396.
Source: arXiv (Cornell University)
Authors: Pätz, Sophie, Sonntag, Martin
Institution: TU Bergakademie Freiberg
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4309046912