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

Joe Robinson
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    I usually hear "relaxation" used in the situation that one or more of the hypotheses are removed while the conclusion remains the same. For example, "if a matrix with integer entries is invertible then its determinant is nonzero" can be relaxed to "if a matrix is invertible then its determinant is nonzero" – JMoravitz Mar 09 '18 at 04:09

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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.

gt6989b
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