标题： 随机图的偶数退化性 显示英文标题

标题： Even-degeneracy of a random graph

摘要： 一个图被称为偶退化图，如果可以通过每一步移除一个偶度顶点的操作，直到最多剩下一条边。最近，Janzer 和 Yip 证明了埃尔德什-瑞尼随机图 $G(n,1/2)$ 在高概率下是偶退化图，并且提出了对于任意一般的 $G(n,p)$，类似的结果是否成立的问题。在本文中，我们通过证明 $G(n,p)$ 在高概率下是偶退化图，从而肯定地回答了这个问题，适用于任意常数 $p\in (0,1)$。 显示英文摘要

摘要： A graph is even-degenerate if one can iteratively remove a vertex of even degree at each step until at most one edge remains. Recently, Janzer and Yip showed that the Erd\H{o}s--Renyi random graph $G(n,1/2)$ is even-degenerate with high probability, and asked whether an analogous result holds for any general $G(n,p)$. In this paper, we answer this question for any constant $p\in (0,1)$ in affirmation by proving that $G(n,p)$ is even-degenerate with high probability.