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I have developed an upper bound on the number of vertices of a particular graph. This bound is the best possible bound that can be found for any given instance. What do you call such a bound? If it were an optimization problem then I would call it the optimal value or the optimal bound. Is that right?

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The phrase you're looking for is tight bound or in your case a tight upper bound.

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  • $\begingroup$ Thanks MGriisser. That definition does not mention whether it is used for one instance of a problem or all instances of it. Not sure but I remember once someone told me if I find an upper bound and be able to find one family of instances of the problem satisfying that upper bound then the upper bound is said to be tight. $\endgroup$ – Opt Oct 30 '17 at 12:44

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