I have some doubts about the correct use of the {XOR} constraint in UML.

I understand how this works in two different ways. Which one is correct?
The xor constraint applies to associations. (either: an object of type A can be associated with 1 object of type C, or: an object of type A can be associated with zero or one object with type B or: an object A can only be on its own, because we have [0 .. 1] near B).
The xor constraint applies to the link (either: an object of type A must be associated with only one object of type C, or: an object of type A must be associated with only one object of type B),
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