Difference between relaxation and generalization

Question

When does one say a theorem/condition relaxes another one, for example in graph theory? Is it the same thing as saying it generalizes?

Answer 1

Usually, generalization means making the same result applicable in a more general circumstance.

On the other hand, relaxing is usually performed on a constraint, and it means removing the constraint from the hypotheses of a particular result.

So you are right, the general idea in what these mean is very similar, in the sense that relaxing constraints makes the results more general, but the connotation of each word is slightly different and so they mean different things.