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

04/29/2021 βˆ™ by Alain Hertz, et al. βˆ™ 0 βˆ™

We study the average number π’œ(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 π’œ(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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