Claims

../

1976_01_01_burr_erdos: Lemma 4.1 of Burr and Erdős (Utilitas Math. 1976) gives Ramsey number 4k-1 for the tree made of a path on four vertices with stars on 2k-1 and k-1 vertices at its ends, classes 2k and k; refereed.

1979_01_01_grossman_harary_klawe: Theorem 2.1 of Grossman, Harary and Klawe (Discrete Math. 1979) gives the double star S(2k-1,k-1), with classes k and 2k, Ramsey number at least 4k for every k >= 4, so the equality 4k minus 1 fails; refereed.

1982_01_01_erdos_faudree_rousseau_schelp: Theorem 2.2 of the 1982 brooms paper (Congr. Numer. 35) gives the broom B_{k,2k}, a star with k leaves on the end of a path on 2k vertices, Ramsey number 4k-1; a proceedings paper, claimed.

2016_05_11_norin_sun_zhao: Theorem 1.3 of the 2016 preprint gives the double star S(2k-1,k-1), with classes k and 2k, Ramsey number at least 4.2k minus o(k), so the equality 4k minus 1 fails for all large k; refereed later work relies on the bound.

2025_09_09_montgomery_pavez_signe_yan: Theorem 1.1 of the 2025 preprint gives R(T) = 4k-1 for every tree with classes 2k and k whose maximum degree is at most 3ck, for a small absolute constant c > 0; claimed.

---