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# Edge Coloring Algorithm Assignment

## Edge Coloring

A graph G = (V, E) how can we color the edges so that edges which share the vertex don't share a color.

### Existing Results

1. Vizing's theorem
• any graph having a maximum vertex degree of δ could be edge colored utilizing for the most part δ + 1 colors.
• Vertex degree: number of edges getting into the actual edge.

### Line Graph

• An Edge Coloring Problem could be formulated like a Vertex Coloring Problem.
• Let L(G) be an auxiliary graph as well as G function as the graphs that all of us want to color. L(G) contains a vertex for each edge in G. There's an edge in L(G) attracted in between two vertices in the event that their own connected edges in G share a vertex.

### Example Auxiliary Graph

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