Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).
A note on the sharp concentration of th e chromatic number of random graphs
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Vector Colorings of Random, Ramanujan, and Large-Girth Irregular Graphs
Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).