Use the Backtracking algorithm for the m-Coloring problem to find all possible colorings of the graph below using the three colors red, green, and white. Show the actions step by step.

For the graph below determine the minimum number of colors necessary to colorits vertices. Justify your answer, by (i) giving a coloring and (ii) explaining why it is not possibleto use fewer colors. You can represent colors by letters a, b, c, .... To show the coloring, mark eachvertex with its color.

If there is an Euler path that starts at AA and ends at some other vertex, give it. Otherwise enter DNE.This should be a list of letters, from A to the other vertex: e.g. ACBDEAD (if that were even possible!). Path:  Since this is a planar graph, the number of regions - arcs + nodes equals what number?

I want a demonstration and explanation step by step of how the answer are made.