As usual, for graphs <FONT FACE=Symbol>G</font>, G, and H, we write <FONT FACE=Symbol>G ®</FONT> (G, H) to mean that any red-blue colouring of the edges of gamma contains a red copy of G or a blue copy of H. A pair of graphs (G, H) is said to be Ramsey-infinite if there are infinitely many minimal graphs F for which we have <FONT FACE=Symbol>G ®</FONT> (G, H). Let l > 4 be an integer. We show that if H is a 2-connected graph that does not contain induced cycles of length at least l, then the pair (Ck,H) is Ramsey-infinite for any k > l, where Ck denotes the cycle of length k.
Ramsey critical graphs; Szemerédi's regularity lemma
