Claims

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1990_04_01_chung_gyarfas_tuza_trotter: Theorem 4 of Chung, Gyárfás, Tuza and Trotter (Discrete Math. 1990) bounds the edges of a 2K_2-free graph of maximum degree D, whence h_2(d) = 5d^2/4 + 1 for even d and (5d^2 - 2d + 1)/4 + 1 for odd d, the t = 2 case; refereed.

2021_03_22_cambie_cames_van_batenburg_de_joannis_de_verclos_kang: The 2022 SIAM J. Discrete Math. paper: h_3(3) = 23, h_t(d) at most 3d^t/2 + 1 for every t, at most d^t + 1 for graphs without a (2t+1)-cycle, and at least 0.629^t d^t for large t and infinitely many d; refereed.

2026_07_02_kumar_mohar_pragada: The July 2026 preprint of Kumar, Mohar and Pragada shows h_3(4) at least 71 and h_3(15) at least 3796, refuting the 2022 formula for h_3(d), and liminf h_3(d)/d^3 at least 253/225, refuting the upper asymptotic at t = 3; unrefereed.

2026_07_29_korsky: Korsky's partial proof claim on the site's tab, later a joint arXiv preprint with Cames van Batenburg, that h_t(d) is at least (1-o(1))d^t as d grows for every t at least 3, by a bipartite construction from complete flags; unrefereed.

2026_08_17_bitterlemma: A thread post and Zenodo manuscript of 17 August 2026 by the Bitter Lemma project claim the exact value h_3(4) = 71, Kumar, Mohar and Pragada's lower bound and a certified finite search in Lean 4, produced with Claude; unreviewed.

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