An odd chordless cycle is a chordless cycle of length 
.
A graph is said to be perfect iff neither the graph 
nor its graph complement 
has an odd chordless cycle. A graph with no 5-cycle and
no larger odd chordless cycle is therefore automatically perfect.
This is true since the presence of a chordless 5-cycle in 
corresponds to a 5-cycle in 
and 
can have no chordless 7-cycle or larger since the diagonals
of these cycles in 
would contain a 5-cycle in 
.
