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https://dx.doi.org/10.48550/ar...
Article . 2024
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Berge pancyclic hypergraphs

Authors: Bailey, Teegan; Li, Yupei; Luo, Ruth;

Berge pancyclic hypergraphs

Abstract

An n n -vertex graph G G is pancyclic if for every ℓ \ell , 3 ≤ ℓ ≤ n 3\leq \ell \leq n , G G contains a cycle of length ℓ \ell . We consider an analog for hypergraphs. An r r -uniform hypergraph is a set of vertices and a set of edges in which every edge contains r r vertices. A Berge cycle of length ℓ \ell in a hypergraph is an alternating sequence of ℓ \ell distinct vertices and ℓ \ell distinct edges v 1 , e 1 , v 2 , … , v ℓ , e ℓ , v 1 v_1,e_1,v_2, \ldots , v_\ell , e_{\ell },v_1 such that { v i , v i + 1 } ⊆ e i \{v_i, v_{i+1}\} \subseteq e_i for all i i , with indices taken modulo ℓ \ell . We similarly call a hypergraph Berge pancyclic if it contains Berge cycles of every possible length. For sufficiently large n n we prove a sharp minimum degree condition guaranteeing Berge pancyclicity in r r -uniform hypergraphs where 3 ≤ r ≤ 3 \leq r \leq ⌊ ( n − 1 ) / 2 ⌋ − 2 \lfloor (n-1)/2\rfloor - 2 . This bound is optimal for all such combinations of n n and r r .

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Keywords

FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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