Anonymous 17 February at Anonymous 18 March at Unknown 13 April at Anonymous 27 April at Unknown 1 May at Anonymous 11 March at Unknown 15 October at Anonymous 19 April at Anonymous 22 September at Wineful thoughts 8 December at Unknown 31 March at Lucky Aldi 26 March at Unknown 6 April at Unknown 7 May at Anonymous 5 May at Unknown 9 May at In this approach using the brute force method, we find all permutations of color combinations that can color the graph.
If any of the permutations is valid for the given graph and colors, we output the result otherwise not. This method is not efficient in terms of time complexity because it finds all colors combinations rather than a single solution. In this approach, we color a single vertex and then move to its adjacent connected vertex to color it with different color. After coloring, we again move to another adjacent vertex that is uncolored and repeat the process until all vertices of the given graph are colored.
In case, we find a vertex that has all adjacent vertices colored and no color is left to make it color different, we backtrack and change the color of the last colored vertices and again proceed further. If by backtracking, we come back to the same vertex from where we started and all colors were tried on it, then it means the given number of colors i. Here backtracking means to stop further recursive calls on adjacent vertices by returning false.
In this algorithm Step Continue — try a different color for current vertex. Backtrack — try a different color for last colored vertex. Here is the solution to the graph coloring problem in C and Java using the backtracking algorithm:. Note: Tb backtrack, we are returning false. By doing so the program comes back to the last recursive call to change the color of the last colored vertex.
If false is returned by the starting vertex then it means there is no solution. In the above program, we have created the same graph as depicted in the first picture and successfully colored the graph using the backtracking algorithm.
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