Size Ramsey numbers for some regular graphs

P. Erdös, R.J. Faudree, C.C. Rousseau and R.H. Schelp [P. Erdös, R.J. Faudree, C.C. Rousseau, R.H. Schelp, The size Ramsey number, Period. Math. Hungar. 9 (1978) 145–161] studied the asymptotic behaviour of rˆ(G,H) for certain graphs G,HG,H. In this paper there will be given a lower bound for the diagonal size Ramsey number of Kn,n,nKn,n,n. The result is a generalization of a theorem for Kn,nKn,n given by P. Erdös and C.C. Rousseau [P. Erdös, C.C. Rousseau, The size Ramsey numbers of a complete bipartite graph, Discrete Math. 113 (1993) 259–262].Moreover, an open question for bounds for size Ramsey number of each nn-regular graph of order n+tn+t for t>n−1t>n−1 is posed.