Given an undirected graph G and a positive integer k, a k-coloring of G means th
ID: 3706888 • Letter: G
Question
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 different 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 exhaustive 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
ANSWER
GIVEN BY
The algorithm is given below:
Set the variables of the linear indoctrination model as “x1, x2, …, xn. Each represent the vertices of the graph G, thus present will be one changeable matching to each of the vertices.
Set the object as make the most of the sum x1+x2+x3+…xn. Now set the constrains: For all xi=1 and xj=1, there should be an edge {xi, xj} in the graph, that is “edge(xi, xj)=1” if xi=1 and xj=1.
The maximal clique will contain those vertices have values 1 in the optimal solution of the linear program.
And the minimum number of colors required are same as the maximal corresponding. Correctness:
The algorithm will give a right output because the maximal group give us in sequence about the main cycle there in the chart which income at least for so as to series we need as a lot of color as the figure of vertices in the series to satisfy the belongings of coloring.
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