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arXiv · 1906.05639

Nearly all cacti are edge intersection hypergraphs of 3-uniform hypergraphs

Martin Sonntag·Hanns-Martin Teichert
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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 ${\cal E}^{EI}=\{e_1 \cap e_2 \ |\ e_1, e_2 \in {\cal E} \ \wedge \ e_1 \neq e_2 \ \wedge \ |e_1 \cap e_2 |\geq2\}$. 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).

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Martin Sonntag, Hanns-Martin Teichert. 2019-06-13. Nearly all cacti are edge intersection hypergraphs of 3-uniform hypergraphs. https://arxiv.org/abs/1906.05639

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