Claims

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1983_03_01_beck: Beck's 1983 theorem (J. Graph Theory) that the size Ramsey number of the path is below 900n for large n, the statement for paths; refereed; the paper is not held, and the bound rests on three printed attestations.

1987_03_01_friedman_pippenger: Friedman and Pippenger (Combinatorica 1987): for fixed d there is a graph with O(n) edges whose every half of the edges contains every n-vertex tree of maximum degree d, so such trees have linear size Ramsey number; refereed.

1995_09_01_haxell_kohayakawa_luczak: Corollary 11 of Haxell, Kohayakawa and Łuczak (1995): the induced size Ramsey number of the cycle is linear in its length for every fixed number of colors, so cycles have linear size Ramsey number; refereed.

2000_02_01_rodl_szemeredi: Theorem 1 of Rödl and Szemerédi (Combinatorica 2000): for large n there is an n-vertex graph of maximum degree 3 whose size Ramsey number is at least c n (log_2 n)^alpha with c, alpha > 0, so the statement fails at d = 3.

2017_01_25_javadi_khoeini_omidi_pokrovskiy: Theorem 1.1 of Javadi, Khoeini, Omidi and Pokrovskiy (Combin. Probab. Comput. 2019): an explicit linear bound on the size Ramsey number of long cycles without the regularity lemma, a second proof for cycles; refereed.

2022_10_11_tikhomirov: Theorem 1.1 of Tikhomirov (Combinatorica 2024; arXiv October 2022): for every n there is an n-vertex graph of maximum degree at most three with size Ramsey number at least c n exp(c sqrt(log n)), a second disproof at d = 3.

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