I think it works with 1 path (checks Faustus...) but there's no telling what the AI is going to do with it. It'll let them land but it won't look right. 4 is always the safe minimum. Yes, 4 paths with 4 vertices.
EDIT: The Faustus has 2 paths, but they are only used once when it launches escape pods. The Moloch, with its 2-foot-square fighterbay, has 3. Everyone else has 4 and up, simply because of the AI's inability to deal with path conflicts. That's why I'm guessing your seeing ships flying away; something else is in the path until it turns to dock.