Welsh-Powell
Order vertices by degree descending. Color each with smallest unused color among neighbors.
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Bound
Uses at most Δ+1 colors (Δ = max degree). Brooks' theorem: except for complete graphs + odd cycles, only Δ colors needed.
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DSatur
Choose next vertex by 'saturation' (distinct colored neighbors). Often better in practice than Welsh-Powell.
Applications
Register allocation in compilers. Frequency assignment in radio. Scheduling exams without conflicts.