Properly colored Hamilton cycles in Dirac-type hypergraphs

DOI10.37236/10651zbMath1510.05220arXiv2006.16544MaRDI QIDQ6344060

Andrzej Ruciński, Sylwia Antoniuk, Nina Kamčev

Publication date: 30 June 2020

Abstract: 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.

Mathematics Subject Classification ID

Hypergraphs (05C65) Eulerian and Hamiltonian graphs (05C45) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40)

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