What is graph coloring?

def greedy_coloring(graph):
    num_vertices = len(graph)
    
    # Initialize a resultant array of size equal to the number of vertices
    # and initialize it with -1 representing no color is assigned to any vertex
    coloring = [-1] * num_vertices
    
    # Assign the first color (0) to the first vertex
    coloring[0] = 0
    
    # Assign colors to the remaining vertices
    for vertex in range(1, num_vertices):
        # Keep a temporary list to track the available colors for each vertex
        # False value of available_colors[c] would mean that the color c is not available
        # because it's assigned to one of its neighbors
        available_colors = [True] * num_vertices
        # Iterate through all neighbors of a vertex and mark their colors as unavailable
        for neighbor in graph[vertex]:
            if coloring[neighbor] != -1:
                available_colors[coloring[neighbor]] = False
        
        # Find the first available color
        color = 0
        while color < num_vertices:
            if available_colors[color]:
                break
            color += 1
        
        # Color the current vertex with the found color
        coloring[vertex] = color
    
    return coloring
def print_graph(graph):
    print("Printing the graph:")
    for v in range(len(graph)):
        print(f"\tVertex {v} is connected to vertices {graph[v]}")
def print_coloring(coloring):
    print("\nPrinting the coloring:")
    for v in range(len(coloring)):
        print(f"\tVertex {v}: Color {coloring[v]}")
def main():
    # A simple example graph represented as adjacency list
    graph = [[1, 2],        # Vertex 0 is connected to vertices 1 and 2
             [0, 2, 3],     # Vertex 1 is connected to vertices 0, 2, and 3
             [0, 1, 3],     # Vertex 2 is connected to vertices 0, 1, and 3
             [1, 2]]        # Vertex 3 is connected to vertices 1 and 2
    # Another example graph represented as adjacency list
    # graph = [[1, 2, 3],     # Vertex 0 is connected to vertices 1, 2, and 3
    #         [0, 2, 4],      # Vertex 1 is connected to vertices 0, 2, and 4
    #         [0, 1, 3, 4],   # Vertex 2 is connected to vertices 0, 1, 3, and 4
    #         [0, 2, 4, 5],   # Vertex 3 is connected to vertices 0, 2, 4, and 5
    #         [1, 2, 3, 5],   # Vertex 4 is connected to vertices 1, 2, 3, and 5
    #         [3, 4, 6, 7],   # Vertex 5 is connected to vertices 3, 4, 6, and 7
    #         [5, 7, 8],      # Vertex 6 is connected to vertices 5, 7, and 8
    #         [5, 6, 8],      # Vertex 7 is connected to vertices 5, 6, and 8
    #         [6, 7]]         # Vertex 8 is connected to vertices 6 and 7
    
    # Print the graph
    print_graph(graph)
    result = greedy_coloring(graph)
    
    # Print the result
    print_coloring(result)
    
if __name__ == "__main__":
    main()

function greedyColoring(graph) {
    const numVertices = graph.length;
    
    // Initialize a resultant array of size equal to the number of vertices
    // and initialize it with -1 representing no color is assigned to any vertex
    const coloring = new Array(numVertices).fill(-1);
    
    // Assign the first color (0) to the first vertex
    coloring[0] = 0;
    
    // Assign colors to the remaining vertices
    for (let vertex = 1; vertex < numVertices; vertex++) {
        // Keep a temporary list to track the available colors for each vertex
        // False value of availableColors[c] would mean that the color c is not available
        // because it's assigned to one of its neighbors
        const availableColors = new Array(numVertices).fill(true);
        // Iterate through all neighbors of a vertex and mark their colors as unavailable
        for (let i = 0; i < graph[vertex].length; i++) {
            const neighbor = graph[vertex][i];
            if (coloring[neighbor] != -1) {
                availableColors[coloring[neighbor]] = false;
            }
        }
        
        // Find the first available color
        let color = 0;
        while (color < numVertices) {
            if (availableColors[color]) {
                break;
            }
            color++;
        }
        
        // Color the current vertex with the found color
        coloring[vertex] = color;
    }
    
    return coloring;
}
function printGraph(graph) {
    console.log("Printing the graph:");
    for (let v = 0; v < graph.length; v++) {
        console.log(`\tVertex ${v} is connected to vertices ${graph[v].join(', ')}`);
    }
}
function printColoring(coloring) {
    console.log("\nPrinting the coloring:");
    for (let v = 0; v < coloring.length; v++) {
        console.log(`\tVertex ${v}: Color ${coloring[v]}`);
    }
}
function main() {
    // A simple example graph represented as adjacency list
    const graph = [
        [1, 2],    // Vertex 0 is connected to vertices 1 and 2
        [0, 2, 3], // Vertex 1 is connected to vertices 0, 2, and 3
        [0, 1, 3], // Vertex 2 is connected to vertices 0, 1, and 3
        [1, 2]     // Vertex 3 is connected to vertices 1 and 2
    ];
    // Another example graph represented as adjacency list
    /*
    const graph = [
        [1, 2, 3],   // Vertex 0 is connected to vertices 1, 2, and 3
        [0, 2, 4],   // Vertex 1 is connected to vertices 0, 2, and 4
        [0, 1, 3, 4],// Vertex 2 is connected to vertices 0, 1, 3, and 4
        [0, 2, 4, 5],// Vertex 3 is connected to vertices 0, 2, 4, and 5
        [1, 2, 3, 5],// Vertex 4 is connected to vertices 1, 2, 3, and 5
        [3, 4, 6, 7],// Vertex 5 is connected to vertices 3, 4, 6, and 7
        [5, 7, 8],   // Vertex 6 is connected to vertices 5, 7, and 8
        [5, 6, 8],   // Vertex 7 is connected to vertices 5, 6, and 8
        [6, 7]       // Vertex 8 is connected to vertices 6 and 7
    ];
    */
    // Print the graph
    printGraph(graph);
    const result = greedyColoring(graph);
    // Print the result
    printColoring(result);
}
main();