论文标题
关于随机树的独立数量
On the independence number of random trees via tricolourations
论文作者
论文摘要
我们对简单生成的树和相关参数（例如它们的匹配数字或邻接矩阵的内核维度）的独立数量感兴趣。我们使用规范的三环形表达这些数量，这是一种用三种颜色为树顶点着色的一种方式。作为应用程序，我们在$ l^p $中获得了限制定理，用于大型简单生成的树（包括大尺寸条件的bienaymé-galton-watson树）中的重态化独立性数字。
We are interested in the independence number of large random simply generated trees and related parameters, such as their matching number or the kernel dimension of their adjacency matrix. We express these quantities using a canonical tricolouration, which is a way to colour the vertices of a tree with three colours. As an application we obtain limit theorems in $L^p$ for the renormalised independence number in large simply generated trees (including large size-conditioned Bienaymé-Galton-Watson trees).
