Size Ramsey Number of Star Forests

Given graphs G, H and F, we say that F is Ramsey for (G, H) and we write F → (G, H), if for every edge coloring of F by red and blue, there is either a red copy of G or a blue copy of H in F. The size Ramsey number rˆ(G, H) is defined as the minimum number of edges of a graph F such that F → (G, H). In 1978, Burr, Erdős, Faudree, Rousseau and Schelp conjectured the exact value of rˆ(G, H), whenever G and H are two arbitrary galaxies. In this talk, we give a partial solution to the conjecture by proving it for many pairs (G, H) of star forests.