Divide and conquer. You must separate your enemies from their allies.

If your enemies go too long without contact with others, they perish.

But you cannot contact them yourself!

To isolate them, pick up and place down paths to prevent contact.

Note: To pick up a path, press the Spacebar while you're traveling on a path. A path cannot be picked up if it will leave a vertex stranded. To place a path, press F while you're at a vertex, then go in the direction of a missing path, and it will be laid down if you're not at the edge of the grid.