1.Implement a Python function called Coloring that takes as input a list of pairs representing the edges of an undirected graph and returns the minimum number of colors needed to color the edges without any two adjacent edges having the same color. The list[ [1,2], [1,3], [3,4], [4,5] ] would return 2.

2. Implement a Python function called Euler that takes as input a list of pairs representing an undirected graph and returns a list presenting a sequence of edges constituting and Euler path if there is one. If no such path exits, return the empty list.

3.Implement a Python function called Hamilton that takes as input a list of pairs representing an undirected graph and returns a list presenting a sequence of edges constituting and Hamiltonian path if there is one. If no such path exits, return the empty list.