The maximum degree of the $r$th power of a sparse random graph
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917635205103616 |
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| author | Frieze, Alan Raut, Aditya |
| author_facet | Frieze, Alan Raut, Aditya |
| contents | Let $G^r_{n,p}$ denote the $r$th power of the random graph $G_{n,p}$, where $p=c/n$ for a positive constant $c$. We prove that w.h.p. the maximum degree $Δ\left(G^r_{n,p}\right)\sim \frac{\log n}{\log_{(r+1)}n}$. Here $\log_{(k)}n$ indicates the repeated application of the log-function $k$ times. So, for example, $\log_{(3)}n=\log\log\log n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximum degree of the $r$th power of a sparse random graph Frieze, Alan Raut, Aditya Combinatorics Let $G^r_{n,p}$ denote the $r$th power of the random graph $G_{n,p}$, where $p=c/n$ for a positive constant $c$. We prove that w.h.p. the maximum degree $Δ\left(G^r_{n,p}\right)\sim \frac{\log n}{\log_{(r+1)}n}$. Here $\log_{(k)}n$ indicates the repeated application of the log-function $k$ times. So, for example, $\log_{(3)}n=\log\log\log n$. |
| title | The maximum degree of the $r$th power of a sparse random graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.06410 |