On the Ramsey numbers for stars versus complete graphs

For graphs G 1 , … , G s , the multicolor Ramsey number R ( G 1 , … , G s ) 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 G i colored with color i , for some 1 ≤ i ≤ s . In this work the multicolor Ramsey number R ( K p 1 , … , K p m , K 1 , q 1 , … , K 1 , q n ) is determined for any set of complete graphs and stars in terms of R ( K p 1 , … , K p m ) .