Almost all graphs with 2:522n edges are not 3-colorable

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Abstract

We prove that for c 2≥522 a random graph with n vertices and m = cn edges is not 3-colorable with probability 1 - o(1). Similar bounds for non-k-colorability are given for k > 3.

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Achlioptas, D., & Molloy, M. (1999). Almost all graphs with 2:522n edges are not 3-colorable. Electronic Journal of Combinatorics, 6(1). https://doi.org/10.37236/1461

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