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  "body": "\n## Summary\n\nThe **Misra \u0026 Gries edge-coloring algorithm** is a polynomial-time algorithm in graph theory that finds an [[edge coloring|0B5WCC02AN]] of any simple graph. The coloring produced uses at most $\\Delta+1$ colors, where $\\Delta$ is the maximum [[degree|0KS0KRDV4Y]] of the graph. This is optimal for some graphs, and it uses at most one color more than optimal for all others. The existence of such a coloring is guaranteed by Vizing's theorem.\n",
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