Use of Matching for Edge Colouring Edges in a matching can share the same colour since matching in a graph is defined as the collection of non-adjacent edges. As a result, we can create an algorithm based on this idea using the below stages. 1. Input: G = (V, E) 2. Output: Minimal edge coloring of G 3. color ← 0 4. while G = ∅ $ 5. find maximal matching M of G 6. color all M vertices with color 7. G ← G − M 8. color ← color + 1 implementation of Python

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.