Graph Coloring

Graph coloring, a classic NP-hard problem, seeks to assign colors to nodes in a graph such that no adjacent nodes share the same color, minimizing the total number of colors used. Current research focuses on improving the efficiency and solution quality of existing algorithms, including greedy heuristics, Monte Carlo Tree Search, and various graph neural network (GNN) architectures, often incorporating techniques like negative message passing or novel loss functions. These advancements are driven by the problem's relevance to diverse applications, such as resource allocation, scheduling, and even brain parcellation in medical imaging, where efficient solutions are crucial for handling large-scale datasets. The development of more powerful and efficient algorithms continues to be a significant area of investigation.