This question is posed by V. Sivaraman in 2018. Clearly f(1) = 1 and f(2) = 2. It is known from [3] that f(3) = 4. Determine f(n) for all n≥4.

[3] M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas, K_4-free graphs with no odd holes, J. Combin. Theory Ser. B 100 (3) (2010) 313–331.