Upper bounds on the average number of colors in the non-equivalent colorings of a graph
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910357566521344 |
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| author | Hertz, Alain Mélot, Hadrien Bonte, Sébastien Devillez, Gauvain Hauweele, Pierre |
| author_facet | Hertz, Alain Mélot, Hadrien Bonte, Sébastien Devillez, Gauvain Hauweele, Pierre |
| contents | A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. Let $\mathcal{A}(G)$ be the average number of colors in the non-equivalent colorings of a graph $G$. We give a general upper bound on $\mathcal{A}(G)$ that is valid for all graphs $G$ and a more precise one for graphs $G$ of order $n$ and maximum degree $Δ(G)\in \{1,2,n-2\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_01120 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Upper bounds on the average number of colors in the non-equivalent colorings of a graph Hertz, Alain Mélot, Hadrien Bonte, Sébastien Devillez, Gauvain Hauweele, Pierre Combinatorics Discrete Mathematics A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. Let $\mathcal{A}(G)$ be the average number of colors in the non-equivalent colorings of a graph $G$. We give a general upper bound on $\mathcal{A}(G)$ that is valid for all graphs $G$ and a more precise one for graphs $G$ of order $n$ and maximum degree $Δ(G)\in \{1,2,n-2\}$. |
| title | Upper bounds on the average number of colors in the non-equivalent colorings of a graph |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2105.01120 |