Graph coloring is the problem of assigning colors to the vertices of a graph such that no two adjacent vertices share the same color. The greedy algorithm is often used for graph coloring, where colors are assigned to each vertex based on a simple rule, such as picking the lowest-numbered available color. Depth-First Search (DFS) can help in exploring the graph, while backtracking can be used to find all possible colorings. Graph coloring is NP-hard in the general case, so approximate or heuristic solutions are often employed in competitive programming. Common graph coloring problems include bipartite checking, chromatic numbers, and scheduling problems.