When setting an anchor on a tree trunk, a simple tension-less knot ("No-Knot") is ideal. Simply wrap the rope around the tree 3 or 4 times and attach the end loosely with a carabineer. This is very strong and maintains nearly 100% of the rope strength. Ropes maintain nearly all of their strength when pulled in nearly a straight line or a very wide arc. Knots create a tight bend and this reduces breaking strength considerably, sometimes as much as 50%. The holding power of simple friction is absolutely amazing. The common eye-splice used on boat ropes is a great example. If the system is failing, you will see the rope slipping. If you need to ditch the anchor, simply unhook the carabineer and unwrap. This is easy since there is no stress on a knot.
You could also create a simple loop like a figure 8 on a bight. With a loop or multiple wraps, leave enough slack to reduce the angle of pull on the carabineer to less than 90°. This greatly reduces the stress on a carabineer.