For large n the unique extremal n-vertex k-chromatic ℓ-connected graph maximizing the number of independent sets is identified via stability; analogous results hold for minimum-degree k-chromatic graphs and for fixed-size independent sets in the 3-chromatic 2-connected case.
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Independent Sets in n-vertex k-chromatic, \ell-connected graphs
For large n the unique extremal n-vertex k-chromatic ℓ-connected graph maximizing the number of independent sets is identified via stability; analogous results hold for minimum-degree k-chromatic graphs and for fixed-size independent sets in the 3-chromatic 2-connected case.