For every graph H with χ(H)=3 the possible values of δ_χ(H,2) form the finite set {1/2, 2/5, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6}, with complete structural classification of the realizing graphs H.
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On the chromatic profile for tripartite graphs and beyond
For every graph H with χ(H)=3 the possible values of δ_χ(H,2) form the finite set {1/2, 2/5, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6}, with complete structural classification of the realizing graphs H.