RESUMO
The graph K j × t is a graph which is complete and multipartite which includes j partite sets and t vertices in each partite set. The multipartite Ramsey number (M-R-number) m j ( G 1 , G 2 , , G n ) is the smallest integer t for the mentioned graphs G 1 , G 2 , , G n , in a way which for each n-edge-coloring ( G 1 , G 2 , , G n ) of the edges of K j × t , G i contains a monochromatic copy of G i for at least one i. The size of M-R-number m j ( n K 2 , C 7 ) for j ≥ 2 , n ≤ 6 , the M-R-number m j ( n K 2 , C 7 ) for j = 2 , 3 , 4 , n ≥ 2 , the M-R-number m j ( n K 2 , C 7 ) for each j ≥ 5 , n ≥ 2 , the M-R-number m j ( C 3 , C 3 , n 1 K 2 , n 2 K 2 , , n i K 2 ) for j ≤ 6 , and i , n i ≥ 1 , and the size of M-R-number m j ( C 3 , C 3 , n K 2 ) for j ≥ 2 and n ≥ 1 have been calculated in various articles hitherto. We acquire some bounds of M-R-number m j ( C 3 , C 3 , n 1 K 2 , n 2 K 2 , , n i K 2 ) in this essay in which i , j ≥ 2 , and n i ≥ 1 , also the size of M-R-number m 4 ( C 3 , C 4 , n K 2 ) for each n ≥ 1 is computed in this paper.