论文标题
大约有很正常的图
Approximately Strongly Regular Graphs
论文作者
论文摘要
我们给出了角链结合的变体，并给出具有类似于强规图的频谱的图形的绝对结合。特别是，我们研究了所谓的大约正规图。 我们将结果应用于极端问题。除其他外，我们显示以下内容： （1）$ \ mathrm {pg}（n，q）$中的上限$，外部点上的割线数不会太大变化，最多具有$ o（q^{\ frac34 n}）$（作为$ q \ rightArrow \ rightArrow \ rightArrow \ infty \ infty \ infty $ n \ rightarrow \ rightarrow \ rightarrow \ rightarrow \ infty \ infty $）。 （2）最佳伪造$ k_m $ - 订单$ v $和度$ k $的图形图形$ i \ i \ leq m-3 $在公共社区上的诱导子图类似于强烈常规的图形，具有$ k = o（v^{1 - \ frac {1- \ frac {1} {1} {1} {1} {3m-2i-5}}}）。
We give variants of the Krein bound and the absolute bound for graphs with a spectrum similar to that of a strongly regular graph. In particular, we investigate what we call approximately strongly regular graphs. We apply our results to extremal problems. Among other things, we show the following: (1) Caps in $\mathrm{PG}(n, q)$ for which the number of secants on exterior points does not vary too much, have size at most $O(q^{\frac34 n})$ (as $q \rightarrow \infty$ or as $n \rightarrow \infty$). (2) Optimally pseudorandom $K_m$-free graphs of order $v$ and degree $k$ for which the induced subgraph on the common neighborhood of a clique of size $i \leq m-3$ is similar to a strongly regular graph, have $k = O(v^{1 - \frac{1}{3m-2i-5}})$.
