Detect perimetral walls of a room

Hi, I’m developing a building editor. Users can draw rooms by adding angles (vertices of the room) with a left click. Clicking on an existing angle closes the room and fills the floor by using the PointInPolygon algorithm.
Let me illustrate the problem. I have this room.

#-----------#
|           |
|           |
|     #-----#
|     |
|     |
|     |
#-----#

Now I want to create another room by connecting two of the vertices like this:

#-----------#
|           |
|           |
|     V--A--X < first click
|     |     |
|     B     | <--new room
|     |     |
#-----Y-----#
      ^
  second click

I need to detect the vertex V and the edges A and B. I tried to implement the convex hull algorithm to find the external walls, but there are degenerated cases where those edges are interior walls… I even tried the Dijstra’s algorithm to find the shortest path between X and Y, but again there are degenerated cases like this:

 first click
      v
      X----------# < second click
      |          |
#-----#-----#    |
|     |     |    | 
|     |     |    | <--new room
|     |     |    |
#-----#-----#    |
      |          |
      Y----------# < third click
      ^
fourth click

How should I approach this problem?

This question was answered here: link text.

Rather than a graph algorithm, you can use a boolean operation to subtract the first room from the second one.