Claims

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1989_08_01_erdos_pach_pollack_tuza: Theorem 2 of Erdős, Pach, Pollack and Tuza (JCTB 1989) bounds the diameter of a connected triangle-free graph by 2n/δ + O(1), the r = 1 instance of part (ii) of the site's wording; refereed, so accepted as a partial claim.

2020_09_05_czabarka_singgih_szekely: Czabarka, Singgih and Székely construct connected K_{2r}-free graphs whose diameter exceeds the conjectured bound for every r at least 2 and every large admissible minimum degree, refuting part (i); refereed.

2025_02_12_cambie_jooken: Cambie and Jooken exhibit 3-colorable graphs of minimum degree 16 whose diameter exceeds the bound of part (i) at r = 2, inside the degree window the first counterexamples left open; a preprint backed by a computer search.

2026_09_03_chen_chen: Chen and Chen announce connected K_{2r+1}-free graphs whose diameter exceeds the bound of part (ii) for every r at least 4, which would refute part (ii) and with it the problem; an unrefereed preprint (arXiv v1).

2026_09_08_kitamura: Kitamura announces Lean proofs that part (ii) fails at r = 3, by a K_7-free family beating the bound by an unbounded margin, and holds at r = 2, and that the amended conjecture holds for k = 3, 4 and fails for k = 5, 6; AI-assisted.

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