A note on the chromatic number of the square of a sparse random graph
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916607058509824 |
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| author | Frieze, Alan Raut, Aditya |
| author_facet | Frieze, Alan Raut, Aditya |
| contents | We show that w.h.p the list chromatic number $χ_\ell$ of the square of $G_{n,p}$ for $p=c/n$ is asymptotically equal to the maximum degree $Δ(G_{n,p})$. Since $χ(G^2_{n,p})\leq χ_\ell(G^2_{n,p})$, this also improves an earlier result of Garapaty et al \cite{KLMP} who proved that $χ(G^2_{n,p}) \leq 6 \cdot Δ(G_{n,p})$ w.h.p. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03563 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on the chromatic number of the square of a sparse random graph Frieze, Alan Raut, Aditya Combinatorics We show that w.h.p the list chromatic number $χ_\ell$ of the square of $G_{n,p}$ for $p=c/n$ is asymptotically equal to the maximum degree $Δ(G_{n,p})$. Since $χ(G^2_{n,p})\leq χ_\ell(G^2_{n,p})$, this also improves an earlier result of Garapaty et al \cite{KLMP} who proved that $χ(G^2_{n,p}) \leq 6 \cdot Δ(G_{n,p})$ w.h.p. |
| title | A note on the chromatic number of the square of a sparse random graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.03563 |