Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).
/T_he Lo v´asz /T_heta Function for Random Reg- ular Graphs and Community Detection in the Hard Regime
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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).