Generalized ramsey theory for graphs, x: double stars

AbstractThe double star S(n, m), where n ⩾ m ⩾ 0, is the graph consisting of the union of two stars K1,n and K1,m together with a line joining their centers. Its ramsey number r(S(n, m)) is the least number p such that there is a monochromatic copy of S(n, m) in any 2-coloring of the edges of Kp. It is shown that r(S(n, m)) = max (2n + 1, n + 2m + 2) if n is odd and m⩽2 and r(S(n, m)) = max (2n + 2, n + 2m + 2) otherwise, for n ⩽ √2m or n ⩾ 3m