AI 中文总结
研究随机诱导P4-free图过程，证明其终端图为平凡完美图，明确终端图连通分支结构分布，推导图参数极限值，发现终端图边数为Θ(n)。
AI 中文摘要
我们研究随机诱导P4-free图过程。设N=组合数n取2，e₁,…,e_N是完全图Kₙ边的均匀随机排列。从空图G₀开始，当Gₘ加eₘ₊₁后不含诱导P4时就添加eₘ₊₁，否则保持图不变。我们证明终端图是平凡完美图，描述了终端图G_N连通分支的结构与分布，由此推导了多个自然图参数的极限值，特别地，终端图G_N有Θ(n)条边。
英文摘要
We study the random induced-$P_4$-free graph process. Let $e_1,\ldots,e_N$, where $N=\binom{n}{2}$, be a uniformly random ordering of the edges of $K_n$. Starting from the empty graph $G_0$, we add $e_{m+1}$ whenever $G_m+e_{m+1}$ contains no induced $P_4$, and otherwise leave the graph unchanged. We show that the terminal graph is a trivially perfect graph and we describe the structure and distribution of the connected components of the terminal graph $G_N$. Consequently, we derive the limiting values of several natural graph parameters. In particular, the terminal graph $G_N$ has $Θ(n)$ edges.
Comments32 pages
