Claims

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1984_03_01_simonovits_sos: Theorem B of the 1984 Combinatorica paper: for t at least 5 and n > ct², the largest number of colors on K_n without a rainbow path on 2t+3+ε₀ vertices is tn − C(t+1,2) + 1 + ε₀, the large-n regime of the path half.

2005_09_01_montellano_ballesteros_neumann_lara: Theorem 5 of the 2005 Graphs and Combinatorics paper: for all n ≥ p ≥ 3 the least number of colors forcing a rainbow p-cycle in K_n is the value E(n,p) conjectured in 1975, so AR(n,C_k) = E(n,k) − 1: the cycle half.

2021_02_01_yuan: Theorem 1 of Yuan's 2021 arXiv preprint gives AR(n,P_k) for all n ≥ k ≥ 5 as the maximum of two terms, the 1975 formula of Erdős, Simonovits and Sós; a preprint the site's curator credits as the proof of the path half.

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