Edge coloring

（重定向自Chromatic index）

Geometric construction of a 7-edge-coloring of the complete graph K8. Each of the seven color classes has one edge from the center to a polygon vertex, and three edges perpendicular to it.

This 3-regular planar graph has 16 vertices and 24 edges, but only 7 edges in any maximum matching. Therefore, it requires four colors in any edge coloring.

A Shannon multigraph with degree six and edge multiplicity three, requiring nine colors in any edge coloring

In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two adjacent edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most $k$ different colors, for a given value of $k$ , or with the fewest possible colors. The minimum required number of colors for the edges of a given graph is called the chromatic index of the graph. For example, the edges of the graph in the illustration can be colored by three colors but cannot be colored by two colors, so the graph shown has chromatic index three.

单词	Chromatic index
释义	Chromatic index 英语百科 Edge coloring （重定向自Chromatic index） In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two adjacent edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most $k$ different colors, for a given value of $k$ , or with the fewest possible colors. The minimum required number of colors for the edges of a given graph is called the chromatic index of the graph. For example, the edges of the graph in the illustration can be colored by three colors but cannot be colored by two colors, so the graph shown has chromatic index three.
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