# example that shows that the edge chromatic number may be larger than the maximal degree

What is an example that shows that the edge chromatic number may be larger than the maximal degree

∆ ≤ X’(G)

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By Brooks' theorem the only examples are odd cycles and complete graphs. – Ross Millikan Feb 13 '13 at 17:09

The cycle on three vertices is one example. Any odd cycle will do.

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