Claims

../

2004_09_01_verstraete: Verstraëte proves that the number of cycle sets on {1,...,n}, the sets of cycle lengths realized by graphs on n vertices, is o(2^(n - n^c)) for an absolute c > 0, so f(n) = o(2^n), the problem's first assertion.

2025_01_17_nenadov: Nenadov shows that graphs on n vertices realize at most 2^(n - n^(1/2 - o(1))) distinct cycle sets, sharpening Verstraëte's bound on the problem's first assertion; published in Combinatorial Theory (2026).

---