A 
-Ramsey graph is a graph
on 
vertices
containing neither a clique of 
vertices nor an independent
vertex set of 
vertices, where 
is the corresponding Ramsey
number and 
(Bondy and Murty 2008, p. 311).
The Ramsey number 
is the least number of vertices
that forces one of these two configurations (Ramsey 1930). Thus a 
-Ramsey graph is an extremal example showing that this
number cannot be reduced. More generally, any graph on
vertices
avoiding both configurations establishes the lower bound 
, but the definition above requires 
.
The cycle graph 
is a 
-Ramsey graph, and the Wagner
graph is a 
-Ramsey
graph. The Paley graph on 17 vertices
is a 
-Ramsey
graph (Bondy and Murty 2008, pp. 310-311). The term denotes a class of extremal
examples rather than a uniquely specified graph.
