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Consider a graph coloring problem where we have a very large graph G = (V,E) whose vertices are to be colored using only 3 distinct colors such that...

Consider a graph coloring problem where we have a very large graph G = (V,E) whose
vertices are to be colored using only 3 distinct colors such that no adjacent node in G has the
same color. Suppose that Alice has found a coloring for G. She thinks it is an achievement
and so would like to communicate this to Bob. But she fears that if Bob comes to know the
coloring of G then she may not get the credit. We need a mechanism by which Bob should be
convinced with a very high probability when Alice has indeed got a satisfying coloring for G.
Note that Alice is trying to convince Bob. So if Alice has got an incorrect coloring then the
probability that Bob accepts the coloring is very low.
Design a suitable mechanism to solve the given problem.

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