 
Summary: On an antiRamsey type result
Noga Alon
, Hanno Lefmann
and Vojtech Ršodl
Abstract
We consider antiRamsey type results. For a given coloring of the kelement subsets of an
nelement set X, where two kelement 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 integers n, n large, the following inequality holds
ck · (ln n)
1
2k1 · n
k1
2k1 inj(k, n) c
k · (ln n)
1
2k1 · n
