Geodesic
Properly colored Hamilton cycles in Dirac-type hypergraphs
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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We consider a robust variant of Dirac-type problems in $k$-uniform hypergraphs. For instance, we prove that if $\mathcal{H}$ is a $k$-uniform hypergraph with minimum codegree at least $\left(\frac 12 + \gamma \right)n$, $\gamma >0$, and $n$ is sufficiently large, then any edge coloring $\phi$ satisfying appropriate local constraints yields a properly colored tight Hamilton cycle in $\mathcal{H}$. Similar results for loose cycles are also shown.
DOI : 10.37236/10651
Classification : 05C65, 05C45, 05D40
Mots-clés : \(k\)-uniform hypergraphs, properly colored tight Hamilton cycle 
@article{10_37236_10651,
     author = {Sylwia Antoniuk and Nina Kam\v{c}ev and Andrzej Ruci\'nski},
     title = {Properly colored {Hamilton} cycles in {Dirac-type} hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {1},
     doi = {10.37236/10651},
     zbl = {1510.05220},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10651/}
}
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Sylwia Antoniuk; Nina Kamčev; Andrzej Ruciński. Properly colored Hamilton cycles in Dirac-type hypergraphs. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/10651

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