标题： 典型的无$T$图表 显示英文标题

标题： Typical $T$-free graphs

摘要： 我们证明了对于每个不是边的树 $T$，对于几乎所有不以 $T$ 为诱导子图的图 $G$，$V(G)$ 可以被划分为认证这一事实的 $\alpha(T)-1$ 个部分。 每个部分诱导出一个 $P_4$-自由图，并且具有进一步依赖于 $T$ 的性质。 因此我们得到了关于不含$T$图的数量的良好界（通常精确到常数因子），并在后续论文~\cite{RY}中表明几乎每个不含$T$的图$G$的色数等于其最大团的大小。 显示英文摘要

摘要： We prove that for every tree $T$ which is not an edge, for almost every graph $G$ which does not contain $T$ as an induced subgraph, $V(G)$ has a partition into $\alpha(T)-1$ parts certifying this fact. Each part induces a graph which is $P_4$-free and has further properties which depend on $T$. As a consequence we obtain good bounds (often tight up to a constant factor) on the number of $T$-free graphs and show in a follow-up paper~\cite{RY} that almost every $T$-free graph $G$ has chromatic number equal to the size of its largest clique.