Problems with guaranteed-to-exist solutions (like this one, & others in PPA, PPAD, etc.) are not NP-complete unless NP = coNP and the Polynomial Hierarchy collapses. Now, we don't yet know that P != NP, or even that P != PH.
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CSI of Charles University
Re: A little more
Problems with guaranteed-to-exist solutions (like this one, & others in PPA, PPAD, etc.) are not NP-complete unless NP = coNP and the Polynomial Hierarchy collapses. Now, we don't yet know that P != NP, or even that P != PH.