The induced Ramsey number 
of two finite simple
graphs is the least number of vertices in a graph 
such that every red-blue coloring of the edges
of 
contains a red induced subgraph isomorphic to
or a blue induced subgraph isomorphic to 
. The copy must be induced in the entire
host graph 
, and all its edges must have
the specified color. The host need not be a complete
graph. For complete graphs, this reduces to
the usual Ramsey number.
The Kohayakawa-Prömel-Rödl conjecture asserts a polynomial bound in the order
of 
when 
is fixed. Zhong et al. (2026) proved 
for 
and 
.
