Loose Hamiltonian Cycles Forced by Large (k-2)-Degree - Approximate Version
Loose Hamiltonian Cycles Forced by Large (k-2)-Degree - Approximate Version
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DOI：
10.1137/16m1065732
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
J. D. O. Bastos;G. Mota;M. Schacht;J. Schnitzer;Fabian Schulenburg
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文献类型：
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作者：
J. D. O. Bastos;G. Mota;M. Schacht;J. Schnitzer;Fabian Schulenburg
本文证明了：对所有的k\geq 4$和1\leq\ell <k/2$，如果k-\ell$能整除n$，则任意n$顶点上的k-一致超图${\mathcal {H}}$包含一个Hamilton圈，其中$\delta_{k-2}（{\mathcal {H}}）\geq（\tfrac{4（k-\ell）-1}{4（k-\ell）^2}+o（1））\binom{n}{2}$。这个度条件是渐近最佳可能的。对于$k=3$的情况，Bus et al.
We prove that for all $k\geq 4$ and $1\leq\ell<k/2$, every $k$-uniform hypergraph ${\mathcal{H}}$ on $n$ vertices with $\delta_{k-2}({\mathcal{H}})\geq(\tfrac{4(k-\ell)-1}{4(k-\ell)^2}+o(1))\binom{n}{2}$ contains a Hamiltonian $\ell$-cycle if $k-\ell$ divides $n$. This degree condition is asymptotically best possible. The case $k=3$ was addressed earlier by Bus et al.