Nearly all cacti are edge intersection hypergraphs of 3-uniform 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 ${\mathcal{E}}^{EI}=\{e_1\cap e_2|e_1,e_2\in \mathcal{E}\wedge e_1\ne e_2\wedge |e_1\cap e_2|\ge 2\}$. Using the so-called clique-fusion, we show that nearly all cacti are edge intersection hypergraphs of 3-uniform hypergraphs. In the proof we make use of known characterizations of the trees and the cycles which are edge intersection hypergraphs of 3-uniform hypergraphs (see arXiv:1901.06292).

9 pages, 3 figures

References in corpus (1)

• Edge intersection hypergraphs - a new hypergraph concept