Something like the following should produce what you want.
tree -d --device / | grep replace-with-correct-device-number
Unfortunately I cannot determine what exactly a "device number" is or how it can be explicitly determined. I can see that on my system my / partition (hda1) is '770' and my /home partition (hda3) is '773'. So, if I wanted to list just the directory tree structure of my /home partition I would use:
tree -d -device / | grep 773
Or, if I wanted to list just my / partition tree structure I would use:
tree -d -device / | grep 770
The whole thing could be dumped to a text file like this:
tree -d -device / | grep 773 > name-of-file.txt
Hope this helps. Hopefully someone will shed some light on the "device number" thing.