Cycles as edge intersection hypergraphs of $k$-uniform hypergraphs ($k \le 6$) -- a constructive approach

Sophie Pätz; Martin Sonntag

paper

Cycles as edge intersection hypergraphs of $k$ -uniform hypergraphs ( $k \leq 6$ ) -- a constructive approach

arXiv:2211.06245

Abstract

If $H = (V, E)$ is a hypergraph, its edge intersection hypergraph $E I (H) = (V, E^{E I})$ has the edge set $E^{E I} = {e_{1} \cap e_{2} ∣ e_{1}, e_{2} \in E \land e_{1} \neq = e_{2} \land ∣ e_{1} \cap e_{2} ∣ \geq 2}$ . In the present paper, we consider 4- and 5-uniform hypergraphs $H$ , respectively, with $E I (H) = C_{n}$ . Our results fill the gap between the 3- and the 6-uniform case considered in arXiv:1902.00396.

17 pages, 10 figures

Cycles as edge intersection hypergraphs of k-uniform hypergraphs (k≤6) -- a constructive approach

Abstract

Cycles as edge intersection hypergraphs of $k$ -uniform hypergraphs ( $k \leq 6$ ) -- a constructive approach