Each edge has a list of allowed colors; a list edge coloring chooses an allowed color on each edge, giving different colors to incident edges. The list-chromatic index is the uniform list-size threshold guaranteeing success.
List edge-coloring is a variation of the standard edge-coloring problem in graph theory, where each edge of a graph has a list of allowable colors from which it can be colored. The objective in list edge-coloring is to assign colors to the edges of the graph in such a way that: 1. No two adjacent edges (i.e., edges that share a common vertex) have the same color. 2. Each edge is colored using a color from its own list of allowable colors.
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