Even-degeneracy of a random graph
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913081474416640 |
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| author | Chao, Ting-Wei Dong, Dingding Xu, Zixuan |
| author_facet | Chao, Ting-Wei Dong, Dingding Xu, Zixuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Even-degeneracy of a random graph Chao, Ting-Wei Dong, Dingding Xu, Zixuan Combinatorics 05C80 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. |
| title | Even-degeneracy of a random graph |
| topic | Combinatorics 05C80 |
| url | https://arxiv.org/abs/2506.01021 |