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One Color Preprocessing Improves DSATUR

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

The Graph Coloring Problem (GCP) is NP-hard and DSATUR stands as one of the fastest heuristics for it despite producing colorings that typically use more colors than state-of-the-art coloring algorithms. We propose SSLD (Semidefinite Spectral Learning with DSATUR), which improves DSATUR by preprocessing a first good color class before letting DSATUR complete coloring the rest of the given graph. We obtain this color class from a Semidefinite Programming (SDP), similar to an SDP used to compute the Lovász theta number. To the best of our knowledge, SSLD is the first approach to improve DSATUR b

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