树的归纳性与普适性
Inducibility and universality for trees
摘要：
我们回答了Bubeck和Linial关于树中子树的极限密度的三个问题。证明了存在正的$\varepsilon_1$和$\varepsilon_2$，使得每棵既不是路也不是星的树最多有诱导数$1-\varepsilon_1$，其中树的诱导数定义为$T$的最大极限密度，并且存在无穷多棵诱导数至少为$\varepsilon_2$的树.最后，我们构造了一个泛树序列，即任何树的极限密度都是正的序列。
英文摘要：
We answer three questions posed by Bubeck and Linial on the limit densities of subtrees in trees. We prove there exist positive $\varepsilon_1$ and $\varepsilon_2$ such that every tree that is neither a path nor a star has inducibility at most $1-\varepsilon_1$, where the inducibility of a tree $T$ is defined as the maximum limit density of $T$, and that there are infinitely many trees with inducibility at least $\varepsilon_2$. Finally, we construct a universal sequence of trees; that is, a sequence in which the limit density of any tree is positive.
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