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On an anti-Ramsey type result , Hanno Lefmann
 

Summary: On an anti-Ramsey type result
Noga Alon
, Hanno Lefmann
and Vojtech Ršodl
Abstract
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 k-element 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
2k-1 · n
k-1
2k-1 inj(k, n) c
k · (ln n)
1
2k-1 · n

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics