论文标题
可分区的分区
Divisible subdivisions
论文作者
论文摘要
我们证明，对于最多$ 3 $的每张图$ h $的最高度$ h $，对于每个正整数$ q $，都有一个有限的$ f = f（h，q）$，这样每一个$ k_f $ -minor都包含$ h $的细分，其中每个边的长度都由其长度换成$ q $。对于循环的情况，我们表明，对于$ f = o（q \ log q）$每个$ k_f $ -minor包含一个长度的周期除以$ q $，并且观察到这解决了弗里德曼的最新问题和第二名作者，关于（弱）扩展图的周期。
We prove that for every graph $H$ of maximum degree at most $3$ and for every positive integer $q$ there is a finite $f=f(H,q)$ such that every $K_f$-minor contains a subdivision of $H$ in which every edge is replaced by a path whose length is divisible by $q$. For the case of cycles we show that for $f=O(q \log q)$ every $K_f$-minor contains a cycle of length divisible by $q$, and observe that this settles a recent problem of Friedman and the second author about cycles in (weakly) expanding graphs.
