On the Ramsey numbers for stars versus complete graphs

AbstractFor graphs G1,…,Gs, the multicolor Ramsey number R(G1,…,Gs) is the smallest integer r such that if we give any edge coloring of the complete graph on r vertices with s colors then there exists a monochromatic copy of Gi colored with color i, for some 1≤i≤s. In this work the multicolor Ramsey number R(Kp1,…,Kpm,K1,q1,…,K1,qn) is determined for any set of complete graphs and stars in terms of R(Kp1,…,Kpm)