A Note on a Conjecture on Niche Hypergraphs View Full Text


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Article Info

DATE

2019-03

AUTHORS

Pawaton Kaemawichanurat, Thiradet Jiarasuksakun

ABSTRACT

For a digraph D, the niche hypergraph NH(D) of D is the hypergraph having the same set of vertices as D and the set of hyperedges E(NH(D))={e⊆V(D):|e|⩾2 and there exists a vertex v such that e=ND−(v) or e=ND+(v)}. A digraph is said to be acyclic if it has no directed cycle as a subdigraph. For a given hypergraph H, the niche number n^(H) is the smallest integer such that H together with n^(H) isolated vertices is the niche hypergraph of an acyclic digraph. C.Garske, M. Sonntag and H.M.Teichert (2016) conjectured that for a linear hypercycle Cm,m⩾2, if min{|e|:e∈E(Cm)}⩾3, then n^(Cm)=0. In this paper, we prove that this conjecture is true. More... »

PAGES

93-97

Identifiers

URI

http://scigraph.springernature.com/pub.10.21136/cmj.2018.0182-17

DOI

http://dx.doi.org/10.21136/cmj.2018.0182-17

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105077054


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