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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.18570 |
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| _version_ | 1866913880055218176 |
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| author | Bona, Miklos Burghart, Fabian Wagner, Stephan |
| author_facet | Bona, Miklos Burghart, Fabian Wagner, Stephan |
| contents | We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson distribution with expected value $2$. This is applied to show a Poisson limit law for the number of common edges in two independent random spanning trees of an Erdős--Rényi random graph $G(n,p)$ for constant~$p$. We also use the same method to prove an analogous result for complete multipartite graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the intersection of pairs of trees Bona, Miklos Burghart, Fabian Wagner, Stephan Combinatorics Probability 05A016, 05A15 We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson distribution with expected value $2$. This is applied to show a Poisson limit law for the number of common edges in two independent random spanning trees of an Erdős--Rényi random graph $G(n,p)$ for constant~$p$. We also use the same method to prove an analogous result for complete multipartite graphs. |
| title | On the intersection of pairs of trees |
| topic | Combinatorics Probability 05A016, 05A15 |
| url | https://arxiv.org/abs/2501.18570 |