Geodesic
Minimum degree conditions for Hamilton \(l\)-cycles in \(k\)-uniform hypergraphs
Jie Han ; Lin Sun1 ; Guanghui Wang
1linsun77@163.com
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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We show that for $ \eta>0 $ and sufficiently large $ n $, every 5-graph on $ n $ vertices with $\delta_{2}(H)\ge (91/216+\eta)\binom{n}{3}$ contains a Hamilton 2-cycle. This minimum 2-degree condition is asymptotically best possible. Moreover, we give some related results on minimum $ d $-degree conditions in $ k $-graphs that guarantee the existence of a Hamilton $ \ell $-cycle when $\ell\le d \le k-1$ and $1\le \ell < k/2$.
DOI : 10.37236/12143
Classification : 05C45, 05C35, 05C07, 05C65
Mots-clés : Dirac thresholds of hypergraphs, \(F\)-tiling

Jie Han    ; Lin Sun  1   ; Guanghui Wang 

1 linsun77@163.com 
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     author = {Jie Han and Lin Sun and Guanghui Wang},
     title = {Minimum degree conditions for {Hamilton} \(l\)-cycles in \(k\)-uniform hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {1},
     doi = {10.37236/12143},
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Jie Han; Lin Sun; Guanghui Wang. Minimum degree conditions for Hamilton \(l\)-cycles in \(k\)-uniform hypergraphs. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/12143

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