Size Ramsey numbers for some regular graphs

P. Erdös, R.J. Faudree, C.C. Rousseau and R.H. Schelp in [Erdös, P., R. J. Faudree, C. C. Rousseau and R. H. Schelp, The size Ramsey number, Period. Math. Hung. 9 (1978), 145–161] studied the asymptotic behaviour of r ˆ ( G , H ) for certain graphs G, H. There will be given some results when each graph of the pair is a regular one. Namely, in this paper a lower bound for the diagonal induced size Ramsey number of each n-regular graph of order n + t for t > 1 is presented. Moreover lower bounds for the diagonal induced size Ramsey number and size Ramsey number of K n , n , n is presented as well. One of the results is a generalization of a theorem for K n , n given by P. Erdös and C.C. Rousseau [Erdös, P., and C. C. Rousseau, The size Ramsey numbers of a complete bipartite graph, Discr. Math. 113 (1993), 259–262].