Claims

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1978_01_01_burr_erdos_faudree_rousseau_schelp: Theorem 1 of Burr, Erdős, Faudree, Rousseau and Schelp (Indag. Math. 1978) gives the size Ramsey number of m copies of one star against n copies of another, the conjectured formula when all stars of each forest are equal.

2002_04_01_gyori_schelp: Theorem 2 of Győri and Schelp (Discrete Math. 2002) proves the star-forest formula whenever the binomial coefficient of each diagonal maximum exceeds the sum of that maximum and all later ones.

2021_11_03_davoodi_javadi_kamranian_raeisi: Theorems 2.3 to 2.6 of Davoodi, Javadi, Kamranian and Raeisi (Ars Math. Contemp. 2025) prove the star-forest formula for one star, two equal stars, all sizes odd, and equal odd stars against a forest with odd largest star.

2026_06_03_fu_luo_ni: The first arXiv version of a June 2026 preprint claimed the size Ramsey formula for all pairs of star forests; the second version, a day later, was retitled and dropped the claim, and the third treats uniform forests.

2026_08_06_cipollini: A three-page AI-assisted argument of August 2026: the size Ramsey number of two star forests is at least the conjectured sum of diagonal maxima minus at most one edge per diagonal; unreviewed, with no journal or review record.

2026_09_04_tienxion: A partial proof claim of September 2026: the star-forest formula holds when every diagonal maximum not attained by an odd pair or a single-edge star is followed by a drop of three, or of two and then two; unreviewed.

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