论文标题
$γ$ - 可变量的一阶附件的一阶逻辑随机图
$γ$-variable first-order logic of uniform attachment random graphs
论文作者
论文摘要
我们研究统一依恋随机图的逻辑极限定律。在此随机图模型中，递归引入了顶点和边缘：在时间$ n+1 $时，将顶点$ n+1 $与$ m $ edge一起引入了新的顶点，并以$ m $不同的顶点从$ 1，\ ldots，n $中随机选择。我们证明，此随机图遵守一阶句子的收敛法，最多使用$ M-2 $变量。
We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with $m$ edges joining the new vertex with $m$ different vertices chosen uniformly at random from $1,\ldots,n$. We prove that this random graph obeys convergence law for first-order sentences with at most $m-2$ variables.
