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 .