Properly colored Hamilton cycles in Dirac-type hypergraphs

We consider a robust variant of Dirac-type problems in \(k\)-uniform hypergraphs. For instance, we prove that if \(H\) is a \(k\)-uniform hypergraph with minimum codegree at least \((1/2 + \gamma )n\), \(\gamma >0\), and \(n\) is sufficiently large, then any edge coloring \(\phi\) satisfying appr...

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Bibliographic Details
Published in:arXiv.org 2020-06
Main Authors: Antoniuk, Sylwia, Kamčev, Nina, Ruciński, Andrzej
Format: Article
Language:English
Subjects:
Graph theory
Graphs
Online Access:Get full text
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Summary:We consider a robust variant of Dirac-type problems in \(k\)-uniform hypergraphs. For instance, we prove that if \(H\) is a \(k\)-uniform hypergraph with minimum codegree at least \((1/2 + \gamma )n\), \(\gamma >0\), and \(n\) is sufficiently large, then any edge coloring \(\phi\) satisfying appropriate local constraints yields a properly colored tight Hamilton cycle in \(H\). Similar results for loose cycles are also shown.
ISSN:2331-8422