论文标题
稀疏随机平面图中最大程度的两个点浓度
Two point concentration of maximum degree in sparse random planar graphs
论文作者
论文摘要
令$ p（n，m）$是从顶点套装的所有平面图$ \ left \ left \ {1，\ ldots，n \ right \} $带有$ m = m = m（n）$ edges上的所有平面图均匀选择的图。我们表明，在稀疏制度中，当$ \ limsup_ {n \ to \ infty} m/n <1 $时，高概率的最高度为$ p（n，m）$，最多为两个不同的值。
Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $\left\{1, \ldots, n\right\}$ with $m=m(n)$ edges. We show that in the sparse regime, when $\limsup_{n \to \infty} m/n<1$, with high probability the maximum degree of $P(n,m)$ takes at most two different values.
