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  "body": "\n## Summary\n\nIn graph theory, **total coloring** is a type of [[graph coloring|0NCPXH194Y]] on the vertices and edges of a graph. When used without any qualification, a total coloring is always assumed to be *proper* in the sense that no adjacent edges, no adjacent vertices and no edge and either endvertex are assigned the same color. The **total chromatic number** $\\chi''(G)$ of a graph $G$ is the fewest colors needed in any total coloring of $G$.\n",
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