Implemented M Coloring Problem (#1562)

* Implemented M Coloring Problem

* Implemented M Coloring Problem

* Switch to a functional approach instead of class-based.
Use proper JSDoc comments.
Refine the comments and remove redundancies.

* Updated Documentation in README.md

* Proper JSDoc comment

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>

Backtracking/MColoringProblem.js

@@ -0,0 +1,49 @@
+/**
+ * Colors a graph using up to m colors such that no two adjacent vertices share the same color.
+ * @param {number[][]} graph - Adjacency matrix of the graph, using 0 for no edge.
+ * @param {number} m - The number of colors to use.
+ * @returns {?Array.<number>} A valid M-coloring of the graph using colors 1 to m, or null if none exists.
+ * @see https://en.wikipedia.org/wiki/Graph_coloring
+ */
+function mColoring(graph, m) {
+  const colors = new Array(graph.length).fill(0);
+
+  // Check if it's safe to color a vertex with a given color.
+  function isSafe(vertex, color) {
+    for (let i = 0; i < graph.length; i++) {
+      if (graph[vertex][i] && colors[i] === color) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  // Use backtracking to try and color the graph.
+  function solveColoring(vertex = 0) {
+    if (vertex === graph.length) {
+      return true;
+    }
+
+    for (let color = 1; color <= m; color++) {
+      if (isSafe(vertex, color)) {
+        colors[vertex] = color;
+        
+        if (solveColoring(vertex + 1)) {
+          return true;
+        }
+
+        // If no solution, backtrack.
+        colors[vertex] = 0;
+      }
+    }
+    return false;
+  }
+
+  // If coloring is possible, return the colors.
+  if (solveColoring()) {
+    return colors;
+  }
+  return null;
+}
+
+export { mColoring };