The paper introduces SSLD, a method that enhances the DSATUR graph‑coloring heuristic by first extracting a high‑quality color class via semidefinite programming. This preprocessing step, inspired by the Lovász theta number, is applied before DSATUR completes the coloring of the remaining graph. Experiments on more than 1,600 benchmark instances—including DIMACS, random, frequency‑assignment, and job‑shop scheduling graphs—show that SSLD matches or outperforms DSATUR in almost all cases, though it is roughly 195 times slower.
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