总着色图算法[关闭]

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如何实现贪心算法来获得图形的完整着色？ 也就是不仅相邻顶点用不同的colors着色，还要用它们顶点的不同colors给边着色？ 尽可能少地使用 colors。 如下图：总着色图

// A C++ program to implement greedy algorithm for graph coloring
#include <iostream>
#include <list>
using namespace std;

// A class that represents an undirected graph
class Graph
{
    int V; // No. of vertices
    list<int> *adj; // A dynamic array of adjacency lists
public:
    // Constructor and destructor
    Graph(int V) { this->V = V; adj = new list<int>[V]; }
    ~Graph()     { delete [] adj; }

    // function to add an edge to graph
    void addEdge(int v, int w);

    // Prints greedy coloring of the vertices
    void greedyColoring();
};

void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w);
    adj[w].push_back(v); // Note: the graph is undirected
}

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

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

    // Initialize remaining V-1 vertices as unassigned
    for (int u = 1; u < V; u++)
        result[u] = -1; // no color is assigned to u

    // A temporary array to store the available colors. True
    // value of available[cr] would mean that the color cr is
    // assigned to one of its adjacent vertices
    bool available[V];
    for (int cr = 0; cr < V; cr++)
        available[cr] = false;

    // Assign colors to remaining V-1 vertices
    for (int u = 1; u < V; u++)
    {
        // Process all adjacent vertices and flag their colors
        // as unavailable
        list<int>::iterator i;
        for (i = adj[u].begin(); i != adj[u].end(); ++i)
            if (result[*i] != -1)
                available[result[*i]] = true;

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

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

        // Reset the values back to false for the next iteration
        for (i = adj[u].begin(); i != adj[u].end(); ++i)
            if (result[*i] != -1)
                available[result[*i]] = false;
    }

    // print the result
    for (int u = 0; u < V; u++)
        cout << "Vertex " << u << " ---> Color "
            << result[u] << endl;
}

// Driver program to test above function
int main()
{
    Graph g1(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);
    cout << "Coloring of graph 1 \n";
    g1.greedyColoring();

    return 0;
}

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

我还想以上面已经提到的方式在 output 中获得这些边缘的 colors