Minimum co-degree threshold for Berge Hamiltonian cycles in hypergraphs
Lu, Linyuan ; Wang, Zhiyu
arXiv, Tome 2019 (2019) no. 0, / Harvested from
We show that for every finite set $R$ of positive integers, there is an integer $n_0=n_0(R)$ such that every $R$-uniform hypergraph $\mathcal{H}$ on $n$ ($n\geq n_0$) vertices with minimum co-degree $\delta_2(\mathcal{H})\geq 1$ contains a Berge cycle $C_s$ for any $3\leq s\leq n$. For $R= \{3\}$, we show that every $3$-graph on $n\geq 7$ vertices with co-degree at least one contains a Hamiltonian Berge cycle. As an application, we determine the maximum Lagrangian of $k$-uniform Berge-$C_{t}$-free hypergraphs and Berge-$P_{t}$-free hypergraphs.
Publié le : 2019-01-17
Classification:  Mathematics - Combinatorics,  05C65, 05C35 
@article{1901.06042,
     author = {Lu, Linyuan and Wang, Zhiyu},
     title = {Minimum co-degree threshold for Berge Hamiltonian cycles in hypergraphs},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.06042}
}

Lu, Linyuan; Wang, Zhiyu. Minimum co-degree threshold for Berge Hamiltonian cycles in hypergraphs. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.06042/