If D = (V,A) is a digraph, its niche hypergraph NH(D) = (V, E) has the edge set ℇ = {e ⊆ V | |e| ≥ 2 ∧ ∃ v ∈ V : e = N−D(v) ∨ e = N+D(v)}. Niche hypergraphs generalize the well-known niche graphs (see [11]) and are closely related to competition hypergraphs (see [40]) as well as double competition hypergraphs (see [33]). We present several properties of niche hypergraphs of acyclic digraphs.
@article{bwmeta1.element.doi-10_7151_dmgt_1893,
author = {Christian Garske and Martin Sonntag and Hanns-Martin Teichert},
title = {Niche Hypergraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {819-832},
zbl = {1350.05112},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1893}
}
Christian Garske; Martin Sonntag; Hanns-Martin Teichert. Niche Hypergraphs. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 819-832. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1893/