AbstractThe size Ramsey number r̂(G, H) of graphsGandHis the smallest integer r̂ such that there is a graphFwith r̂ edges and if the edge set ofFis red‐blue colored, there exists either a red copy ofGor a blue copy ofHinF. This article shows that r̂(Tnd, Tnd) ⩽c·d2· n andc·n3⩽ r̂(Kn, Tnd) ⩽c(d)·n3log n for every tree Tndon n vertices. and maximal degree at most d and a complete graphKnonnvertices. A generalization will be given. Probabilistic method is used throught this paper. © 1993 Joh