Berge Pancyclic hypergraphs
Teegan Bailey, Yupei Li, Ruth Luo

TL;DR
This paper establishes a sharp minimum degree condition for uniform hypergraphs to contain Berge cycles of all lengths from 3 to n, thus guaranteeing pancyclicity.
Contribution
It proves a new Dirac-type theorem that characterizes when an r-uniform hypergraph is pancyclic based on minimum degree thresholds.
Findings
Hypergraphs with minimum degree above a specific threshold are pancyclic.
The result is sharp for large n and certain uniformities r.
Provides a new criterion for cycle existence in hypergraphs.
Abstract
A Berge cycle of length in a hypergraph is an alternating sequence of distinct vertices and distinct edges such that for all , with indices taken modulo . We call an -vertex hypergraph pancyclic if it contains Berge cycles of every length from to . We prove a sharp Dirac-type result guaranteeing pancyclicity in uniform hypergraphs: for , , if is an -vertex, -uniform hypergraph with minimum degree at least , then is pancyclic.
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Taxonomy
TopicsGraph theory and applications
