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Miklós Schweitzer 2008, Problem 1

Source: Miklós Schweitzer 2008

July 30, 2016

college contestsMiklos Schweitzerfunction

Problem Statement

Let

H \subset P(X)

be a system of subsets of

X

and

\kappa > 0

be a cardinal number such that every

x \in X

is contained in less than

\kappa

members of

H

. Prove that there exists an

f \colon X \rightarrow \kappa

coloring, such that every nonempty

A \in H

has a “unique” point, that is, an element

x \in A

such that

f(x) \neq f(y)

for all

x \neq y \in A

.
(translated by Miklós Maróti)

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