For all H with χ(H)=3, δ_χ(H,2) belongs to the finite set {1/2, 2/5, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6}, with complete structural characterization of the associated H and an extension to color-critical graphs via the new vertex-extendable threshold.
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On the chromatic profile for tripartite graphs and beyond
For all H with χ(H)=3, δ_χ(H,2) belongs to the finite set {1/2, 2/5, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6}, with complete structural characterization of the associated H and an extension to color-critical graphs via the new vertex-extendable threshold.