Claims

../

2016_02_24_day_johnson: Day and Johnson (J. Combin. Theory Ser. B 124, 2017) give n-colorings of K_(2^n+1) with long shortest monochromatic odd cycles, so f(n) tends to infinity, at least 2^(sqrt(2 log2 n) - O(1)); refereed.

2024_12_10_girao_hunter: Girão and Hunter (arXiv preprint, 2024) prove that every n-coloring of K_(2^n+1) has a monochromatic odd cycle of length at most (2^n+1)/n^(1-epsilon) for fixed epsilon > 0 and large n; a preprint.

2025_06_17_janzer_yip: Janzer and Yip (Math. Proc. Cambridge Philos. Soc. 181, 2026) prove that every n-coloring of K_(2^n+1) has a monochromatic odd cycle of length O(n^(3/2) 2^(n/2)); refereed.

2026_09_25_cai: A partial proof claim on the site's tab (25 September 2026): R(3,3,3) = 17 gives a 3-coloring of K_9 with no monochromatic triangle, and a structural argument with a finite enumeration and a SAT check gives f(3) = 5; unreviewed.

---