Universality of the matching number in percolated regular graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913736063713280 |
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| author | Diskin, Sahar Kang, Mihyun Lichev, Lyuben |
| author_facet | Diskin, Sahar Kang, Mihyun Lichev, Lyuben |
| contents | Fix a sequence of $d$-regular graphs $(G_d)_{d\in \mathbb{N}}$ and denote by $G_{d,p}$ the graph obtained from $G_d$ after edge-percolation with probability $p=c/d$, for a constant $c>0$. We prove a quantitative local convergence of $(G_{d,p})_{d\in \mathbb{N}}$. In combination with results of Bordenave, Lelarge and Salez, it implies that the rescaled matching number of $G_{d,p}$ is asymptotically equivalent to that of the binomial random graph $G(n,c/n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality of the matching number in percolated regular graphs Diskin, Sahar Kang, Mihyun Lichev, Lyuben Combinatorics Probability Fix a sequence of $d$-regular graphs $(G_d)_{d\in \mathbb{N}}$ and denote by $G_{d,p}$ the graph obtained from $G_d$ after edge-percolation with probability $p=c/d$, for a constant $c>0$. We prove a quantitative local convergence of $(G_{d,p})_{d\in \mathbb{N}}$. In combination with results of Bordenave, Lelarge and Salez, it implies that the rescaled matching number of $G_{d,p}$ is asymptotically equivalent to that of the binomial random graph $G(n,c/n)$. |
| title | Universality of the matching number in percolated regular graphs |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2503.11242 |