Tutorial : https://www.youtube.com/watch?v=Cl3A_9hokjU

Color Assignment: [0, 1, 2, 1, 3]

Color Assignment: [0, 1, 3, 1, 2]

Color Assignment: [0, 2, 1, 2, 3]

Color Assignment: [0, 2, 3, 2, 1]

Color Assignment: [0, 3, 1, 3, 2]

Color Assignment: [0, 3, 2, 3, 1]

**Source:**import java.util.*; import java.io.*; import java.math.*; public class GraphColoring { static int connected[][]; static int[] colors; static int nColors; static int nNodes; static int getNodeColor(int k){ do{ int j; //Assign the next color colors[k] = colors[k]+1; //If all colors have been tested on this node, //return because there are no more new colors left //to be considered for this node if(colors[k]==nColors+1)return 0; //Check to see if some connected node already has this color for(j=1;j<=nNodes;++j){ if(connected[k][j] == 1 && colors[k] == colors[j] && k!=j){ break; } } if(j==nNodes+1)return colors[k]; }while(true); } static void mColoring(int k){ do{ //get a color for this node colors[k] = getNodeColor(k); //if no more colors can be applied to this node, return if(colors[k] == 0)return; //if all the nodes have been assigned colors successfully, print the color assignments if(k==nNodes){System.out.println("Color Assignment: "+Arrays.toString(colors)); //return /*don't quit until all possible assignments have been found*/ } //consider the next node else mColoring(k+1); }while(true); } public static void main(String[] args) throws Exception{ nColors = 3; connected = new int[][]{ {0, 0, 0, 0, 0}, {0, 1, 1, 0, 1}, {0, 1, 1, 1, 1}, {0, 0, 1, 1, 1}, {0, 1, 1, 1, 1}, }; nNodes = connected.length-1; colors = new int[nNodes+1]; mColoring(1); } }

**Output:**Color Assignment: [0, 1, 2, 1, 3]

Color Assignment: [0, 1, 3, 1, 2]

Color Assignment: [0, 2, 1, 2, 3]

Color Assignment: [0, 2, 3, 2, 1]

Color Assignment: [0, 3, 1, 3, 2]

Color Assignment: [0, 3, 2, 3, 1]

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