M-Coloring Problem Statement

Given an undirected graph as an adjacency matrix and an integer M, determine whether you can color the vertices of the graph using at most M colors such that no two adjacent vertices share the same color.

Example:

Input:

adjacencyMatrix = [
[0, 1, 0],
[1, 0, 1],
[0, 1, 0]
], M = 3

Output:

"YES"

Explanation:

The adjacency matrix indicates that vertex 1 is connected to vertex 2, and vertex 2 is connected to vertex 3. It is possible to color the graph using 2 colors (e.g., coloring vertex 1 with color 2, vertex 2 with color 1, and vertex 3 with color 2), which is ≤ M.

Constraints:

1 ≤ T ≤ 1000

1 ≤ V ≤ 20

1 ≤ M ≤ V

Time Limit: 1 sec

Question

M-Coloring Problem Statement

Given an undirected graph as an adjacency matrix and an integer M, determine whether you can color the vertices of the graph using at most M colors such that no two adjacent vertices share the same color.

Example:

Input:

adjacencyMatrix = [
[0, 1, 0],
[1, 0, 1],
[0, 1, 0]
], M = 3

Output:

"YES"

Explanation:

The adjacency matrix indicates that vertex 1 is connected to vertex 2, and vertex 2 is connected to vertex 3. It is possible to color the graph using 2 colors (e.g., coloring vertex 1 with color 2, vertex 2 with color 1, and vertex 3 with color 2), which is ≤ M.

Constraints:

1 ≤ T ≤ 1000
1 ≤ V ≤ 20
1 ≤ M ≤ V
Time Limit: 1 sec

Accepted Answer

The M-Coloring Problem involves coloring the vertices of a graph using at most M colors such that no two adjacent vertices share the same color.

Check if the graph can be colored using at most M colors without any adjacent vertices sharing the same color.
Use backtracking or graph coloring algorithms to solve the problem efficiently.
Ensure that the number of colors used is less than or equal to M.
Consider the constraints provided to optimize the solution.
Example: If adjacencyMatrix = [[0, 1, 0], [1, 0, 1], [0, 1, 0]], M = 3, the output should be 'YES'.