This paper investigates the application of stable matching algorithms to partial graph matching tasks in a supervised learning setting. While traditional stable matching algorithms are known to be computationally efficient, they typically optimize outcomes for only one set of elements in a bipartite matching problem. We first discuss on the optimality of a matching in partial graph matching and demonstrate that the single-sided optimality limitation in stable matching can be overcome in a learning-based setting. We propose a novel partial graph matching framework founded on stable matching principles and evaluate its performance on standard benchmarks. Our experimental results show that the proposed framework achieves comparable results to state-of-the-art partial graph matching techniques while maintaining computational efficiency. While the choice of partial matching technique may vary depending on specific requirements, theoretical and empirical analyses in this study highlight the potential of incorporating stable matching paradigms in the development of future partial graph matching techniques.