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Rainbow Berge Hamiltonicity in edge-colored random $k$-uniform hypergraphs — arXiv:2609.01989

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.01989
License (as archived): CC0-1.0
Archived: 2026-10-17T05:32:53.550Z
SHA-256 of the archived text: 89c15074405fbc3c27ef55ab6bf83ac9a231f0157a1bb8f485ec002c6ce32680
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How to cite

Rainbow Berge Hamiltonicity in edge-colored random $k$-uniform hypergraphs — arXiv:2609.01989 — arXiv (en), https://arxiv.org/abs/2609.01989 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dfbbdefca1d5 (Metraipolis archive dc_dfbbdefca1d5, sha256 89c15074405fbc3c27ef55ab6bf83ac9a231f0157a1bb8f485ec002c6ce32680)

BibTeX

@misc{dcdfbbdefca1d5,
  title = {Rainbow Berge Hamiltonicity in edge-colored random $k$-uniform hypergraphs — arXiv:2609.01989},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.01989},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dfbbdefca1d5; sha256 89c15074405fbc3c27ef55ab6bf83ac9a231f0157a1bb8f485ec002c6ce32680},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.01989. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $H \sim H^{k}_c(n,p)$ be an edge-colored random $k$-uniform hypergraph on the vertex set $[n]$, where each edge $e \in \binom{[n]}{k}$ is included independently with probability $p$ and is uniformly and independently assigned a color from the color set $[c]$. For $k = 2$, Ferber and Krivelevich (2016) established that if $c = (1+o(1))n$ and $p = (\log n + \log \log n + \omega(n))/n$, then with high probability the edge-colored random graph $H \sim H^2_c(n,p)$ contains a rainbow Hamilton Berge cycle. Subsequently, Bal, Berkowitz, Devlin, and Schacht (2021) determined the threshold for the appearance of a (non-rainbow) Hamilton Berge cycle in random $k$-uniform hypergraphs. In this paper, we generalize the results to all integers $k \ge 3$. We prove that if $c = (1+o(1))n$ and $p = (k-1)! \frac{\log n + \log\log n + \omega(n)}{n^{k-1}}$, then with high probability $H \sim H^{k}_c(n,p)$ contains a rainbow Hamilton Berge cycle. Furthermore, both conditions on $c$ and $p$ are asymptotically tight. \noindent\emph{Key words:} Rainbow subgraph, Hamiltonicity, Berge cycle, Random hypergraph.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-03 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.01989 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T04:59:51.767Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-03?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).