Minimum degree thresholds for Hamilton $(\ell,k-\ell)$-cycles in $k$-uniform hypergraphs
| Autor: | Wang, Jian, You, Jie |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $n>k>\ell$ be positive integers. We say a $k$-uniform hypergraph $\mathcal{H}$ contains a Hamilton $(\ell,k-\ell)$-cycle if there is a partition $(L_0,R_0,L_1,R_1,\ldots,L_{t-1},R_{t-1})$ of $V(\mathcal{H})$ with $|L_i|=\ell$, $|R_i|=k-\ell$ such that $L_i\cup R_i$ and $R_i\cup L_{i+1}$ (subscripts module $t$) are all edges of $\mathcal{H}$ for $i=0,1,\ldots,t-1$. In the present paper, we determine the tight minimum $\ell$-degree condition that guarantees the existence of a Hamilton $(\ell,k-\ell)$-cycle in every $k$-uniform $n$-vertex hypergraph for $k\geq 7$, $k/2\leq \ell\leq k-1$ and sufficiently large $n\in k\mathbb{N}$. Comment: 19 pages. arXiv admin note: substantial text overlap with arXiv:2002.12234 by other authors |
| Databáze: | arXiv |
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