A weakly perfect graph is a graph for which (without any requirement that this condition
also hold on induced subgraphs, which is required for a graph to be perfect),
where
is the clique number and is the chromatic number.
Maimani, H. R.; Pournaki, M. ä.; and Yassemi, S. "A Class of Weakly Perfect Graphs." Czech. Math. J.60,
1037-1041, 2010.Sloane, N. J. A. Sequence A198634
in "The On-Line Encyclopedia of Integer Sequences."
(without any requirement that this condition
also hold on induced subgraphs, which is required for a graph to be perfect),
where 
is the clique number and 
is the chromatic number.
, 2, ... nodes are 1, 2, 4, 11, 33, 152, 1006, 11805, ...
(OEIS A198634).
