m-покраска говном

#include <iostream>
#include <vector>

using namespace std;

class Graph {
    vector<vector<int>> g;
    vector<int> color;
    int c;

    bool isValid(int v){
        for (int i = 0; i < g[v].size(); i++){
            if (color[g[v][i]] == color[v])
                return false;
        }
        return true;
    }

public:

    Graph(int _n, int _c, vector<vector<int>> &_g){
        g = _g;
        color.resize(_n, -1);
        c = _c;
    }

    void Solve(int v = 0){
        if (v == g.size()){
            cout << "YES\n";
            exit(0);
        } else {
            for (int i = 0; i < c; i++){
                color[v] = i;
                if (isValid(v))
                    Solve(v + 1);
                color[v] = 0;
            }
        }
    }

};

int main() {
    int n, m, c;
    cin >> n >> m >> c;
    vector<vector<int>> g(n);
    for (int i = 0; i < m; i++) {
        int fr, to;
        cin >> fr >> to;
        fr--;
        to--;
        g[fr].emplace_back(to);
        g[to].emplace_back(fr);
    }

    Graph graph(n, c, g);
    g.clear();

    graph.Solve();

    cout << "NO\n";

}