Please work the part a) and part b) of the question! Thank you! 1. Given an undi
ID: 3700776 • Letter: P
Question
Please work the part a) and part b) of the question! Thank you!
1. Given an undirected graph G and a positive integer k, a k-coloring of G means that every vertex of G is assigned one of the integers 1 through k in such a way that for every edge in the graph, the two vertices of the edge are assigned different values. (Think of the integers 1 through k as representing k diferent colors. We are trying to color the vertices so that no edge connects two vertices that have the same color) a) Outline an algorithm for searching for a k-coloring of a graph. The input to the algorithm is a graph G and the integer k. You can use a recursive algorithm that implements an search for a solution (with lots of pruning). b) An exhaustive search might not be feasible for a large graph. Pick a heuristic search technique, either simulated annealing or genetic algorithms, and discuss in general terms how it could be applied to this particular problem.Explanation / Answer
Solution:
The algorithm is given below:
Correctness:
The algorithm will give a correct output because the maximal clique gives us information about the biggest cycle present in the graph which means at least for that cycle we need as many colors as the number of vertices in the cycle to satisfy the property of coloring.
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