Claims

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1981_06_01_hindman: Hindman shows, with a computer check, that an edge-disjoint union of n copies of K_n has chromatic number n for every n at most 10 (Canad. J. Math. 1981); the site gives the range as n < 10.

2007_01_01_romero_sanchez_arroyo: Romero and Sánchez-Arroyo prove the conjecture for intersecting linear hypergraphs whose edges can be numbered so that the labels at each vertex form at most two runs of consecutive integers (Ars Combin. 2007).

2016_05_11_araujo_pardo_vazquez_avila: Araujo-Pardo and Vázquez-Ávila prove the conjecture for the arithmetic decompositions of K_n with different central vertices, an infinite class of n-quasiclusters (Ars Combin. 2016).

2020_10_12_alesandroni: Alesandroni proves that a linear n-uniform hypergraph with n edges has chromatic number n when, for each k from 2 up to the square root of n, at most k squared of its vertices have degree k (Discrete Math. 2021).

2021_01_12_kang_kelly_kuhn_methuku_osthus: For every sufficiently large n, an edge-disjoint union of n copies of K_n has chromatic number n (Ann. of Math. 2023); the threshold is not computed, and the site reads the remaining finite range of n as decidable.

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