Reproduce “Faster Exact Algorithms for 3- and 4-Coloring: Deterministic Improvements and Further Randomized Speedups” on OpenResearch
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About this paper
Ryosuke Yamano, Tetsuo Shibuya
The authors improve worst-case upper bounds for exact 3-coloring and 4-coloring on arbitrary graphs. For 3-coloring, they combine high-degree forest structure with constraint-satisfaction solving and decomposition-based dynamic programming. For 4-coloring, they retain earlier branching and improve terminal-case solvers. Deterministic and randomized bounds improve prior results, but do not show randomization is necessary. These are asymptotic guarantees, not measured runtimes.
Summary by alphaXiv.
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