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Claim. The double star $S(n,m)$, $n\ge m\ge0$, is the union of the stars $K_{1,n}$ and $K_{1,m}$ with a line joining their centers (p. 247), a tree on $N=n+m+2$ vertices. Theorem 3.1 (p. 249) of the paper on the library's [[../library/ramsey_theory/grossman_1979_generalized_ramsey_theory_graphs_x_double_stars/_index|source card]] reads: "The ramsey numbers of the double stars satisfy $r(S(n,m))\le2n+m+2$." Since $2n+m+2\le2n+2m+2=2N-2$, every double star satisfies the bound of the problem. Theorem 3.3 (p. 250) gives the exact value for $n\ge3m$, the site's $R(S_{t_1,t_2})=2t_1$ for $t_1\ge3t_2-2$ in its notation, which disproves Burr's exact conjecture for trees.

Covers. The corrected Statement of Problem 547 for every double star, including the stars $S(n,0)=K_{1,n+1}$ on at least three vertices. Every other tree is outside this claim; the full corrected Statement is settled by the accepted claim page [[problems/ramsey_theory/E0547/claims/2026_09_03_adamczewski|the 2026 claim]].

Depends on. Nothing in this wiki; the result is the paper's own theorem.

Acceptance. Refereed: J. W. Grossman, F. Harary and M. Klawe, Generalized Ramsey theory for graphs, X: double stars, Discrete Math. 28 (1979), no. 3, 247--254, doi:10.1016/0012-365X(79)90132-8, received 8 May 1978 and revised 22 May 1979; this page's date is the first day of the volume's year. No reviewed evidence is listed: the site's label DECIDABLE settles neither the problem nor any part of it.