The 
-color
vertex Ramsey class 
of a finite nonempty graph 
is the class of graphs 
for which every vertex coloring
with 
colors contains a subgraph isomorphic
to 
whose vertices all have the same color. These colorings need not be proper. The induced vertex
Ramsey class 
instead requires a vertex-induced subgraph
of this kind.
Axenovich and Schmitteckert (2026) proved that for any two nonisomorphic finite nonempty graphs 
and every positive integer 
,
 |
and likewise
 |
Thus either type of vertex Ramsey class determines its defining graph up to graph isomorphism.
