Even-degeneracy of a random graph

TL;DR

This paper proves that for any constant probability p between 0 and 1, the Erdős–Rényi random graph G(n,p) is almost surely even-degenerate, extending previous results for G(n,1/2).

Contribution

It generalizes the high-probability even-degeneracy property from G(n,1/2) to all G(n,p) with constant p in (0,1).

Findings

G(n,p) is even-degenerate with high probability for all constant p in (0,1).

Extends previous results from p=1/2 to all constant p.

Confirms the robustness of even-degeneracy in random graphs.

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 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.