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arXiv · 2506.01021

Even-degeneracy of a random graph

Ting-Wei Chao·Dingding Dong·Zixuan Xu
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Abstract

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 Erdős--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.

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Ting-Wei Chao, Dingding Dong, Zixuan Xu. 2026-05-01. Even-degeneracy of a random graph. https://arxiv.org/abs/2506.01021

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