A coupling is a set of ridges two to two independent: they do not share peaks.
Perfect coupling: Each top of the graph is in exactly one stop of coupling
A perfect graph has an even number of peaks (the reciprocal is not true)
A perfect coupling is a coupling of maximum size (impossible to enlarge, you can not pair more), the reciprocal is not true.
Example of use: In a logistics company, employees have one or more permits allowing them to drive a certain type of vehicle. The problem can be represented in a graph with the company's employees and vehicles as its top. To solve the problem you then have to find a pairing of max size.
Gluttonous algorithm to find maximum coupling:
Step 1: A stop is randomly selected and stored in a copy of the graph (left)
Step 2: Stop stops that are incidental at both summits are removed and another stop is selected randomly
Step 3: Stop stops that are incidental at both peaks are removed, resulting in maximum coupling