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### This function takes two inputs: one a graph, and the other a coloring of the vertices, and determines whether or not the coloring is a proper vertex-coloring of the given graph

INSTRUCTIONS TO CANDIDATES

You will create two Python functions:

• is proper: This function takes two inputs: one a graph, and the other a coloring of the vertices, and determines whether or not the coloring is a proper vertex-coloring of the given graph.

Examples:

is_proper({“A” : [“B”, “C”], “B” : [“A”, “C”], “C” : [“A”, “B”]}, {“A” : 1, “B” : 2, “C” : 3}) should return True

is_proper({“A” : [“B”, “C”], “B” : [“A”, “C”], “C” : [“A”, “B”]}, {“A” : 1, “B” : 1, “C” : 3}) should return False

• greedy: This function takes two inputs: one a graph, and the other an ordering of the vertices as a list, and returns the proper vertex-coloring produced by the greedy algorithm over the ordering in the list

Examples:

greedy({“A” : [“B”,“C”],“B” : [“A”],“C” : [“A”]},[“A”,“B”,“C”]) should return {“A” : 1,“B” : 2,“C” : 2}

greedy({“A” : [“B”],“B” : [“A”,“C”],“C” : [“B”,“D”],“D” : [“C”]},[“A”,“D”,“B”,“C”]) should return {“A” : 1,“B” : 2,“C” : 3,“D” : 1}.

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