Strong Ramsey theorems for Steiner systems

Jaroslav Nešetřil, Vojtěch R{ödl
1987 Transactions of the American Mathematical Society  
It is shown that the class of partial Steiner (fc, Z)-systems has the edge Ramsey property, i.e., we prove that for every partial Steiner (k, i)-system Q there exists a partial Steiner (fc, Z)-system )i such that for every partition of the edges of H into two classes one can find an induced monochromatic copy of Q. As an application we get that the class of all graphs without cycles of lengths 3 and 4 has the edge Ramsey property. This solves a longstanding problem in the area.
doi:10.1090/s0002-9947-1987-0896015-8 fatcat:dibu7ctchvgpfltsiedqq3jjom