We show that the exclusivity (E) principle singles out the set of quantum
correlations associated to any exclusivity graph assuming the set of quantum
correlations for the complementary graph. Moreover, we prove that, for
self-complementary graphs, the E principle, by itself (i.e., without further
assumptions), excludes any set of correlations strictly larger than the quantum
set. Finally, we prove that, for vertex-transitive graphs, the E principle
singles out the maximum value for the quantum correlations assuming only the
quantum maximum for the complementary graph. This opens the door for testing
the impossibility of higher-than-quantum correlations in experiments.Comment: REVTeX4, 4 pages, one new result (Result 2) and two new authors,
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