Question

Write an algorithm that does a minimum vertex coloring on a graph. In Java

Answer 1

Program:
import java.io.*;
import java.util.*;
import java.util.LinkedList;

// This class represents an undirected graph using adjacency list
class Graph
{
   private int V; // No. of vertices
   private LinkedList<Integer> adj[]; //Adjacency List

   //Constructor
   Graph(int v)
   {
       V = v;
       adj = new LinkedList[v];
       for (int i=0; i<v; ++i)
           adj[i] = new LinkedList();
   }

   //Function to add an edge into the graph
   void addEdge(int v,int w)
   {
       adj[v].add(w);
       adj[w].add(v); //Graph is undirected
   }

   // Assigns colors (starting from 0) to all vertices and
   // prints the assignment of colors
   void greedyColoring()
   {
       int result[] = new int[V];

       // Initialize all vertices as unassigned
       Arrays.fill(result, -1);

       // Assign the first color to first vertex
       result[0] = 0;

       // A temporary array to store the available colors. False
       // value of available[cr] would mean that the color cr is
       // assigned to one of its adjacent vertices
       boolean available[] = new boolean[V];
      
       // Initially, all colors are available
       Arrays.fill(available, true);

       // Assign colors to remaining V-1 vertices
       for (int u = 1; u < V; u++)
       {
           // Process all adjacent vertices and flag their colors
           // as unavailable
           Iterator<Integer> it = adj[u].iterator() ;
           while (it.hasNext())
           {
               int i = it.next();
               if (result[i] != -1)
                   available[result[i]] = false;
           }

           // Find the first available color
           int cr;
           for (cr = 0; cr < V; cr++){
               if (available[cr])
                   break;
           }

           result[u] = cr; // Assign the found color

           // Reset the values back to true for the next iteration
           Arrays.fill(available, true);
       }

       // print the result
       for (int u = 0; u < V; u++)
           System.out.println("Vertex " + u + " ---> Color "
                               + result[u]);
   }

   // Driver method
   public static void main(String args[])
   {
       Graph g1 = new Graph(5);
       g1.addEdge(0, 1);
       g1.addEdge(0, 2);
       g1.addEdge(1, 2);
       g1.addEdge(1, 3);
       g1.addEdge(2, 3);
       g1.addEdge(3, 4);
       System.out.println("Coloring of graph 1");
       g1.greedyColoring();

       System.out.println();
       Graph g2 = new Graph(5);
       g2.addEdge(0, 1);
       g2.addEdge(0, 2);
       g2.addEdge(1, 2);
       g2.addEdge(1, 4);
       g2.addEdge(2, 4);
       g2.addEdge(4, 3);
       System.out.println("Coloring of graph 2 ");
       g2.greedyColoring();
   }
}

Sample output:

Coloring of graph 1
Vertex 0 --->  Color 0
Vertex 1 --->  Color 1
Vertex 2 --->  Color 2
Vertex 3 --->  Color 0
Vertex 4 --->  Color 1

Coloring of graph 2
Vertex 0 --->  Color 0
Vertex 1 --->  Color 1
Vertex 2 --->  Color 2
Vertex 3 --->  Color 0
Vertex 4 --->  Color 3