To some extent, yes.  Suppose you want to use the technique of running around, remembering everything you've seen, then spotting the first duplication.  If you're not allowed to mark the nodes then you need to create and maintain some sort of external data structure to remember everything you've seen.  Space complexity O(n), time complexity depends on the techniques, but since you have no information about the size then you can assume O(n log n).<p>But the space complexity is the killer, so let's assume you can mark each node.  If the mark starts off in a known state then you're OK and the algorithm is trivial.<p>So what if you don't know the starting state of the mark on each node?  That means you have to run around the list once, setting each mark to a known state.  But how do you know when you're done?  There might be a loop, so you need a loop detection algorithm.<p>So even if you're allowed to mark the nodes this is non-trivial.