论文标题
超图的链色链
Chain method for panchromatic colorings of hypergraphs
论文作者
论文摘要
我们处理有关超图的全天色着色的极端问题。如果每个边缘都符合每种颜色，则hypergraph $ h $的顶点$ r $颜色是\ emph {panchronic}。我们证明，每$ 3 <r \ leq \ sqrt [3] {n/（100 \ ln n）} $，每个$ n $ n $ siform-siform HyperGraph $ h $ at $ | e（H） {r-1} {r}} \ left（\ frac {r} {r-1} \ right）^{n-1} $具有带有$ r $颜色的Panchronic Cornoring。
We deal with an extremal problem concerning panchromatic colorings of hypergraphs. A vertex $r$-coloring of a hypergraph $H$ is \emph{panchromatic} if every edge meets every color. We prove that for every $3<r\leq\sqrt[3]{n/(100\ln n)}$, every $n$-uniform hypergraph $H$ with $|E(H)|\leq \frac{1}{20r^2}\left(\frac{n}{\ln n}\right)^{\frac {r-1}{r}}\left(\frac{r}{r-1}\right)^{n-1}$ has a panchromatic coloring with $r$ colors.
