论文标题
旋塞图子图中的最大程度
Maximal degrees in subgraphs of Kneser graphs
论文作者
论文摘要
在本文中，我们研究了neser图$ kg（n，k）$的非空诱导子图的最高学位。主要结果之一断言，对于$ k> k_0 $和$ n> 64k^2 $，每当非空子图具有$ m \ ge k k {n-2} $ vertices时，其最高学位至少为$ \ frac 12（1- \ frac {1- \ frac {k^2} n）m- $ $ $ $ $ {这本质上是最好的。中间步骤之一是获得最高程度较小的非空尺寸的结构性结果。
In this paper, we study the maximum degree in non-empty induced subgraphs of the Kneser graph $KG(n,k)$. One of the main results asserts that, for $k>k_0$ and $n>64k^2$, whenever a non-empty subgraph has $m\ge k{n-2\choose k-2}$ vertices, its maximum degree is at least $\frac 12(1-\frac {k^2}n) m - {n-2\choose k-2}\ge 0.49 m$. This bound is essentially best possible. One of the intermediate steps is to obtain structural results on non-empty subgraphs with small maximum degree.
