Lower Bounds and properties for the average number of colors in the non-equivalent colorings of a graph
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911791049605120 |
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| author | Hertz, Alain Mélot, Hadrien Bonte, Sébastien Devillez, Gauvain |
| author_facet | Hertz, Alain Mélot, Hadrien Bonte, Sébastien Devillez, Gauvain |
| contents | We study the average number $\mathcal{A}(G)$ of colors in the non-equivalent colorings of a graph $G$. We show some general properties of this graph invariant and determine its value for some classes of graphs. We then conjecture several lower bounds on $\mathcal{A}(G)$ and prove that these conjectures are true for specific classes of graphs such as triangulated graphs and graphs with maximum degree at most 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_14172 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Lower Bounds and properties for the average number of colors in the non-equivalent colorings of a graph Hertz, Alain Mélot, Hadrien Bonte, Sébastien Devillez, Gauvain Combinatorics Discrete Mathematics We study the average number $\mathcal{A}(G)$ of colors in the non-equivalent colorings of a graph $G$. We show some general properties of this graph invariant and determine its value for some classes of graphs. We then conjecture several lower bounds on $\mathcal{A}(G)$ and prove that these conjectures are true for specific classes of graphs such as triangulated graphs and graphs with maximum degree at most 2. |
| title | Lower Bounds and properties for the average number of colors in the non-equivalent colorings of a graph |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2104.14172 |