Abstract
The Ramsey number r= r( G 1- G 2-⋯- G m , H 1- H 2-⋯- H n ) denotes the smallest r such that every 2-coloring of the edges of the complete graph K r contains a subgraph G i with all edges of one color, of a subgraph H i with all edges of a second color. These Ramsey numbers are determined for all sets of graphs with at most four vertices, and in the diagonal case ( m= n, G i = H i ) for all pairs of graphs, one with at most four and the other with five vertices, so as for all sets of graphs with five vertices.
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