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arXiv · 2104.14172

Lower Bounds and properties for the average number of colors in the non-equivalent colorings of a graph

Alain Hertz·Hadrien Mélot·Sébastien Bonte·Gauvain Devillez
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Abstract

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.

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Alain Hertz, Hadrien Mélot, Sébastien Bonte, Gauvain Devillez. 2021-04-29. Lower Bounds and properties for the average number of colors in the non-equivalent colorings of a graph. https://doi.org/10.1016/j.dam.2022.08.011

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