For the decomposition of a graph representing a map, I’m trying to use different algorithms to select the edge to remove.

The question is:

• When you have multiple valid choices, which is the best edge to select … if any?

Some basic rules are:

• Avoid new F5 to be created
• Get rid of F5 whenever is possible, selecting the edge of a face with 2, 3 or 4 edges
• Consider to remove an edge from an F5 face only if no faces with 2, 3, 4 edges exist

Here are all possibilities. Last 2 groups (removing edges from F5 and F6) don’t have to be taken into account. I just wanted to see how it continued after the cases with faces made of 2, 3, 4 and 5 edges: