... triangle need not exist). If x 2 = y then there is a K3-path joining xand y, a contradiction. If x 2 = y then x 2 is incident with the edge of E1, otherwise there exists a (K1 ,2 ,K3)-decomposition, ... papers dealing with the problem of determining the set R(F, H). For example, Burr, Erd˝os and Lov´asz [1] proved that R(2K 2 , 2K 2 )={3K 2 ,C5} andR(K1 ,2 ,K1 ,2 )={K1,3,C2n+1} for n ≥ 1. ... contradiction.Case 2. Theedgese1,e 2 are incident.W.l.o.g assume that e1= v1v 2 and e 2 = v 2 v3.LetT1= v1v 2 y be the triangle whichcontains e1such that y = x 2 and T 2 = v 2 v3z be the triangle...