A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let Hk(n,m) be a random k-uniform hypergraph on n vertices formed by picking m edges uniformly, independently and with replacement. It is easy to show that if r ≥ rc = 2k-1 ln 2 - (ln 2)/2, then with high probability Hk(n,m = rn) is not 2-colorable. We complement this observation by proving that if r ≤ rc - 1 then with high probability Hk(n,m = rn) is 2-colorable.
CITATION STYLE
Achlioptas, D., & Moore, C. (2002). On the 2-colorability of random hypergraphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2483, pp. 78–90). Springer Verlag. https://doi.org/10.1007/3-540-45726-7_7
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