论文标题
线性光谱图兰问题，用于具有给定色数的图表的扩展
Linear spectral Turan problems for expansions of graphs with given chromatic number
论文作者
论文摘要
$ r $均匀的超图是线性的，如果每两个边缘最多在一个顶点中相交。图$ f $的$ r $ expansion $ f^{r} $是$ r $均匀的超图，从$ f $获得的$ f $获得的每个边缘从$ f $的每个边缘放大了$ f $的每个边缘，$ r-2 $ diss的顶点$ r-r-2 $ disttex从$ f $的$ f $的顶点分离中，例如，分离的差异会被脱离差异。 Let $ex_{r}^{lin}(n,F^{r})$ and $spex_{r}^{lin}(n,F^{r})$ be the maximum number of edges and the maximum spectral radius of all $F^{r}$-free linear $r$-uniform hypergraphs with $n$ vertices, respectively.在本文中，我们介绍了$ ex_ {r}^{lin}（n，f^{r}）$和$ spex_ {r} {r}^{lin，n，f^{r}）$的尖锐（或渐近）界限（n，f^{r}）$带有色数$ k $的图形。
An $r$-uniform hypergraph is linear if every two edges intersect in at most one vertex. The $r$-expansion $F^{r}$ of a graph $F$ is the $r$-uniform hypergraph obtained from $F$ by enlarging each edge of $F$ with a vertex subset of size $r-2$ disjoint from the vertex set of $F$ such that distinct edges are enlarged by disjoint subsets. Let $ex_{r}^{lin}(n,F^{r})$ and $spex_{r}^{lin}(n,F^{r})$ be the maximum number of edges and the maximum spectral radius of all $F^{r}$-free linear $r$-uniform hypergraphs with $n$ vertices, respectively. In this paper, we present the sharp (or asymptotic) bounds of $ex_{r}^{lin}( n,F^{r})$ and $spex_{r}^{lin}(n,F^{r})$ by establishing the connection between the spectral radii of linear hypergraphs and those of their shadow graphs, where $F$ is a $(k+1)$-color critical graph or a graph with chromatic number $k$.
