Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).
An alon-boppana ty pe bound for weighted graphs and lower- bounds for spectral sparsification
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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).