A weakly perfect graph is a finite simple graph for which induced
subgraphs , which is required for a graph to be perfect ),
where clique number and chromatic number .
All perfect graphs are weakly perfect.
The numbers of nonisomorphic weakly perfect graphs on nodes are 1, 2, 4, 11, 33, 152, 1006, 11805,
... (OEIS A198634 ).
See also Chromatic Number ,
Clique Number ,
Perfect Graph ,
Strongly
Perfect Graph
Explore with Wolfram|Alpha
References Maimani, H. R.; Pournaki, M. R.; 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." Referenced
on Wolfram|Alpha Weakly Perfect Graph
Cite this as:
Weisstein, Eric W. "Weakly Perfect Graph."
From MathWorld https://mathworld.wolfram.com/WeaklyPerfectGraph.html
Subject classifications More... Less...
(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).
