完全グラフでエッジカラーリングを実行するC++プログラム

完全グラフは、頂点の任意のペアの間に接続エッジがあるグラフです。これは、完全グラフでエッジカラーリングを実行するためのC++プログラムです。

アルゴリズム

Begin
   Take the input of the number of vertices ‘n’.
   Construct a complete graph using e=n*(n-1)/2 edges, in ed[][].
   Function EdgeColor() is used to Color the graph edges.
   A) Assign color to current edge as c i.e. 1 initially.
   B) If the same color is occupied by any of the adjacent edges, then
      discard this color and go to flag again and try next color.
   C) Print the color for each edge.
End

例

#include<iostream>
using namespace std;
void EdgeColor(int ed[][3], int e) {
   int i, c, j;
   for(i = 0; i < e; i++) {
      c = 1; //assign color to current edge as c i.e. 1 initially.
      flag:
         ed[i][2] = c;
         //If the same color is occupied by any of the adjacent edges, then
         discard this color and go to flag again and try next color.
         for(j = 0; j < e; j++) {
            if(j == i)
               continue;
               if(ed[j][0] == ed[i][0] || ed[j][0] == ed[i][1] || ed[j][1] == ed[i][0] || ed[j][1] == ed[i][1]) {
                  if(ed[j][2] == ed[i][2]) {
                     c++;
                     goto flag;
                  }
               }
         }
   }
}
int main() {
   int i, n, e, j, cnt = 0;
   cout<<"Enter the number of vertexes for the complete graph: ";
   cin>>n;
   e = (n*(n-1))/2;
   int ed[e][3];
   for(i = 1; i <= n; i++) {
      for(j = i+1; j <= n; j++) {
         ed[cnt][0] = i;
         ed[cnt][1] = j;
         ed[cnt][2] = -1;
         cnt++;
      }
   }
   EdgeColor(ed , e);
   for(i = 0; i < e; i++)
      cout<<"\nThe color of the edge between vertex
      n1):"<<ed[i][0]<<" and n(2):"<<ed[i][1]<<" is: color"<<ed[i][2]<<".";
}

出力

Enter the number of vertexes for the complete graph: 4
The color of the edge between vertex n(1):1 and n(2):2 is: color1.
The color of the edge between vertex n(1):1 and n(2):3 is: color2.
The color of the edge between vertex n(1):1 and n(2):4 is: color3.
The color of the edge between vertex n(1):2 and n(2):3 is: color3.
The color of the edge between vertex n(1):2 and n(2):4 is: color2.
The color of the edge between vertex n(1):3 and n(2):4 is: color1.