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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