We consider anti-Ramsey type results. For a given coloring ∆ of the k-element subsets of an n-element set X, where two k-element sets with nonempty intersection are colored differently, let inj∆(k, n) be the largest size of a subset Y ⊆ X, such that the kelement subsets of Y are colored pairwise differently. Taking the minimum over all colorings, i.e. inj(k, n) = min∆ {inj∆(k, n)}, it is shown that for every positive integer k there exist positive constants ck, c ∗ k > 0 such that for all… CONTINUE READING