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arXiv · 1901.06292

Edge intersection hypergraphs - a new hypergraph concept

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 ${\cal E}^{EI}=\{e_1 \cap e_2 \ |\ e_1, e_2 \in {\cal E} \ \wedge \ e_1 \neq e_2 \ \wedge \ |e_1 \cap e_2 |\geq2\}$. Besides investigating several structural properties of edge intersection hypergraphs, we prove that all trees but seven exceptional ones are edge intersection hypergraphs of 3-uniform hypergraphs.

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Martin Sonntag, Hanns-Martin Teichert. 2019-01-18. Edge intersection hypergraphs - a new hypergraph concept. https://arxiv.org/abs/1901.06292

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