Properly colored Hamilton cycles in Dirac-type hypergraphs
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.16544
- arXiv:
- arXiv:2006.16544
- Bibcode:
- 2020arXiv200616544A
- Keywords:
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- Mathematics - Combinatorics;
- 05C65;
- 05C45;
- 05D40