Exploring Multi-View Graph Neural Network (MV-GNN) for Graph Coloring

Abstract

The Graph Coloring Problem (GCP), which involves determining the chromatic number or the minimum number of colors needed to color neighboring nodes in a graph, is a critical computational challenge with applications in scheduling, resource allocation, and frequency assignment. Heuristic-based algorithms like Artificial Bee Colony (ABC), Sequential Coloring Algorithm (SCA), Welsh–Powell Algorithm (WPA), Branch-and-Cut, Greedy, Dsatur, RLF, and others are commonly used to tackle this problem, but they are computationally expensive and often do not yield optimal solutions. Given the graph-structured nature of the problem, graph-based models such as Graph Neural Networks (GNNs) have proven to be highly advantageous. In this research, we extend GNNs to Multi-View Graph Neural Networks (MV-GNNs) to address the GCP. By leveraging multiple perspectives of a graph, our approach incorporates distinct views to learn node embeddings and predict optimal color assignments. Through extensive experiments and comparisons with existing state-of-the-art algorithms, we demonstrate that MV-GNNs can efficiently determine the chromatic number of large graphs, achieving competitive performance in coloring accuracy, scalability, and computational efficiency. This work represents a foundational step in applying multi-view learning paradigms to solve NP-complete problems.