3 problems

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Conjectured minimum degree threshold for Hamilton $ell$ -cycles
For $k\ge3$ , $1\le\ell<k/2$ , and $k-\ell\le d\le k-1$ , let $h_d^\ell(k)$ be the limiting normalized minimum $d$ -degree threshold for Hamilton $\ell$ -cycles. Let $t(k,d,\ell)$ be th…
Conjecturesolvedextremal-combinatorics hypergraph-hamilton-cycles hypergraph-tilingsarXiv posted 2 days ago
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The vertex-degree conjecture for loose Hamilton cycles
Buss–Han–Schacht conjecture.
Conjectureopendegree-conditions hypergraph-hamilton-cyclesarXiv posted 2 days ago
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The extremal construction conjecture for Hamilton $l$ -cycles
Extremal construction conjecture. The construction $H_0$ is an extremal configuration for Hamilton $l$ -cycles whenever $k-l$ does not divide $k$ .
Conjectureopenextremal-combinatorics hypergraph-hamilton-cyclesarXiv posted 2 days ago

Conjectured minimum degree threshold for Hamilton ellellell-cycles