#### M Coloring Problem

P
```/**
* 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 }
```