The simplest way to do this is to use the low bit of the address (so long as you align your memory to at least 2 bytes this is fine as all addresses will end in 0) as a marker for whether you've already visited that pointer.
And yes, you're correct that GCs handle cycles without issue (that's a large part of the reason to use tracing GC over other memory management strategies like ObjC's auto-reference counting).
Don't know if any GCs use it, but if modifying the pointers is not possible then one alternative is Floyd's cycle-finding algorithm[1] which uses constant storage (two pointers).
"Finding cycles" is not really the problem a GC is trying to solve. It's trying to find all of the non-reachable data, across a possibly cyclic graph. It just has to ensure that it doesn't loop infinitely while traversing that graph.
I purposefully used the word 'efficient' in my original post. Of course you can find cycles many ways, but floyd's (or similar) are not acceptably fast and never can be in general.
See https://en.wikipedia.org/wiki/Tracing_garbage_collection#Na%...
And yes, you're correct that GCs handle cycles without issue (that's a large part of the reason to use tracing GC over other memory management strategies like ObjC's auto-reference counting).