论文标题
线性森林的两分turan数量和光谱极差
The bipartite Turan number and spectral extremum for linear forests
论文作者
论文摘要
图$ h $的两部分Turán数量，由$ ex（m，n; h）$表示，是任何两部分图中的最大边数$ g =（x，y; e）$，带有$ | x | = m $和$ | y | y | y | = n $，不包含$ h $ h $ as a sex exgraph。在本文中，我们确定了$ ex（m，n; f _ {\ ell}）$ for nutary $ \ ell $，并适当大的$ n $，与$ m $和$ \ ell $相比，其中$ f_ \ ell $是一条线性森林，由$ \ ell $ $ ell $ $ pertertex distex distex distex distex distex。而且，极端图已被表征。此外，这些结果用于获得两分图的最大光谱半径，该光谱不包含$ f _ {\ ell} $作为子图，并表征所有达到最大光谱半径的极端图。
The bipartite Turán number of a graph $H$, denoted by $ex(m,n; H)$, is the maximum number of edges in any bipartite graph $G=(X,Y; E)$ with $|X|=m$ and $|Y|=n$ which does not contain $H$ as a subgraph. In this paper, we determined $ex(m,n; F_{\ell})$ for arbitrary $\ell$ and appropriately large $n$ with comparing to $m$ and $\ell$, where $F_\ell$ is a linear forest which consists of $\ell$ vertex disjoint paths. Moreover, the extremal graphs have been characterized. Furthermore, these results are used to obtain the maximum spectral radius of bipartite graphs which does not contain $F_{\ell}$ as a subgraph and characterize all extremal graphs which attain the maximum spectral radius.
