So we just learned about self-reducibility in class. My professor and our textbook would not commit to saying that all problems in NP are self-reducible, but there didn't seem to be any examples of problems that are not. I was wondering if there are any examples, or if it's just a situation where you can't prove a negative easily. Wikipedia only says
It is conjectured that the integer factorization problem is not self-reducible.
Googling found one result, which seems to state that planar graph 4 coloring is not self-reducible because LF-k coloring for a planar graph reduces to that reduction, but I couldn't quite follow the proof right now.
Is this an actual example of a self-reducibility disproof, and are there others?