论文标题
稀疏随机外平面图中的巨型组件和2核
The giant component and 2-core in sparse random outerplanar graphs
论文作者
论文摘要
令$ a（n，m）$是从所有顶点标记的外平面图和带有$ n $顶点和$ m $ edge的所有顶点标记的外平面图中随机选择的图。当$ m = n/2+s $ for $ s = o（n）$时，我们考虑稀疏制度中的$ a（n，m）$。我们表明，使用高概率，$ a（n，m）$中的巨型组件以$ m = n/2+o \ left（n^{2/3} \ right）$出现，并确定2核的典型顺序。此外，我们证明，如果$ s =ω\ left（n^{2/3} \ right）$，则概率很高，$ a（n，m）$中的每个边缘最多属于一个周期。
Let $A(n,m)$ be a graph chosen uniformly at random from the class of all vertex-labelled outerplanar graphs with $n$ vertices and $m$ edges. We consider $A(n,m)$ in the sparse regime when $m=n/2+s$ for $s=o(n)$. We show that with high probability the giant component in $A(n,m)$ emerges at $m=n/2+O\left(n^{2/3}\right)$ and determine the typical order of the 2-core. In addition, we prove that if $s=ω\left(n^{2/3}\right)$, with high probability every edge in $A(n,m)$ belongs to at most one cycle.
