Claims

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1963_01_01_erdos: Erdős's Theorem 1 of 1963: every family of at most 2^(n-1) n-element sets has property B, so m(n) > 2^(n-1), and m(n) > (1-eps) 2^n log 2 for large n; the first lower bound for Problem 901, refereed.

1964_09_01_erdos: Erdős's Theorem 1 of 1964: a greedy choice of n-sets in a ground set of 2n^2 points gives a non-2-colorable n-uniform hypergraph with at most n^2 2^(n+1) edges, so m(n) <= n^2 2^(n+1), still the best upper bound.

1977_01_01_beck: Beck's 1977 paper proves m(n) > c (log n) 2^n, so m(n)/2^n tends to infinity, as Erdős and Lovász had conjectured; the first lower bound beyond the 2^n scale for Problem 901, refereed.

1978_01_01_beck: Beck's 1978 paper proves that every n-uniform hypergraph with at most n^(1/3-g(n)) 2^n edges is 2-colorable for some g(n) tending to zero, so m(n) > n^(1/3-o(1)) 2^n; the lower bound for Problem 901 until 2000.

2000_01_01_radhakrishnan_srinivasan: For all large n, every n-uniform hypergraph with at most 0.7 sqrt(n/ln n) 2^n edges is 2-colorable, so m(n) > 0.7 sqrt(n/ln n) 2^n: the best lower bound for Problem 901, refereed.

2009_02_10_pluhar: Pluhár's Corollary 1 of 2009: a greedy coloring along a random vertex order shows m(n) > 0.5268 n^(1/4) 2^n for n >= 3, a two-page proof that m(n)/2^n tends to infinity; weaker than the best bound, refereed.

2014_01_01_ostergard: An exhaustive computer search shows that the least number of edges of a 4-uniform hypergraph without property B is 23, closing the earlier range 21 <= m(4) <= 23; the value the site lists for Problem 901, refereed.

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