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I think there is a mistake in a solution. Solution Review: Graph Coloring

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#1

Solution works incorrectly for this case. There should be 2 colors.
Graph g3(4);
g3.addEdge(0, 2);
g3.addEdge(2, 3);
g3.addEdge(3, 1);
cout << “\nColoring of graph 3 \n”;
g3.greedyColoring();

Course: https://www.educative.io/collection/5642554087309312/5745541363269632
Lesson: https://www.educative.io/collection/page/5642554087309312/5745541363269632/4722020770119680

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#2

Hello @Olga_Sabirova,

Thank you for sharing this query. You’ve shared quite an interesting boundary case that evaluates whether the coloring process is correctly followed by the defined algorithm or not. At first glance, it does look like there should be only two colors:

Vertex 0 ---> Color 0
Vertex 1 ---> Color 1
Vertex 2 ---> Color 1
Vertex 3 ---> Color 0

But, as the process does not directly go back to color a vertex after all others are considered. Instead, it sequentially considers each vertex and assigns the first available color based on the current state. This output demonstrates the algorithm’s effort to minimize the number of colors used while ensuring no two adjacent vertices share the same color. The greedy algorithm does not always find the most optimal solution (minimum number of colors) but provides a feasible solution quickly. So the actual output from the code is correct, that is:

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

The key points to take away are:

  • The greedy algorithm assigns colors in a sequential manner, considering the vertices’ ordering and the graph’s structure.
  • It ensures no two adjacent vertices have the same color by checking the colors of adjacent vertices and choosing the lowest-numbered unused color.
  • The algorithm’s efficiency and the number of colors used can depend on the graph’s structure and the order in which vertices are considered.

The output for your given test case is correct based on the graph structure and the edges defined in the solution lesson. It reflects the expected behavior of the greedy coloring algorithm for the given graph. I hope this explanation helps in understanding how the assignment of colors is handled in the solution code.

Feel free to share more suggestions and feedback. We’d be happy to help. Thanks!

Happy learning!