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edited Jun 9, 2015 at 21:48

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What is the best lower bound in terms of $k$ on the number of edges in a $3$-uniform hypergraph that is not $k$-colorable?

Thanks in advance.

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asked Jun 9, 2015 at 20:30

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Is it true that any $3$-uniform hypergraph that is not $k$-colorable must have $\Omega(k^3)$ edges?

What is the best lower bound in terms of $k$ on the number of edges in a $3$-uniform hypergraph that is not $k$-colorable?

co.combinatorics graph-theory graph-colorings hypergraph