METHOD1: Well, then it depends on your segues, if all of them is push type, then your green VC will be embedded too. If it is, then you can navigate through all your hierarchy via [self.navigationController popToViewController:desiredViewController animated:YES]
.
Here what this method does: Pops view controllers until the specified view controller is at the top of the navigation stack.
Reference: UINavigationController Class
METHOD2: If you still want to use modal presentation, you could create weak delegate
property to bind your greenController with controller, which presented it (or use NSNotificationCenter to listen your dismiss modal view controller event). Once user pressed on dismissing, controller which presented greenController redirects it with no animation to yellow one. It will create the illusion that once you dismissed your controller underneath is yellowController. However, it still depends on your transition needs between yellow-green controllers.