On a problem of Erdős and Lovász on coloring non-uniform hypergraphs
نویسنده
چکیده
Let f(r) = minH P F∈E(H) 1 2|F | , where H ranges over all 3-chromatic hypergraphs with minimum edge cardinality r. Erdős-Lovász (1975) conjectured f(r) → ∞ as r → ∞. This conjecture was proved by Beck in 1978. Here we show a new proof for this conjecture with a better lower bound: f(r) ≥ ( 1 16 − o(1)) ln r ln ln r .
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