Graph-theoretic problems arise in real-world applications like logistics, communication networks, and traffic optimization. These problems are often complex, noisy, and irregular, posing challenges for traditional algorithms. Large language models (LLMs) offer potential solutions but face challenges, including limited accuracy and input length constraints. To address these challenges, we propose MA-GTS (Multi-Agent Graph Theory Solver), a multi-agent framework that decomposes these complex problems through agent collaboration. MA-GTS maps the implicitly expressed text-based graph data into clear, structured graph representations and dynamically selects the most suitable algorithm based on problem constraints and graph structure scale. This approach ensures that the solution process remains efficient and the resulting reasoning path is interpretable. We validate MA-GTS using the G-REAL dataset, a real-world-inspired graph theory dataset we created. Experimental results show that MA-GTS outperforms state-of-the-art approaches in terms of efficiency, accuracy, and scalability, with strong results across multiple benchmarks (G-REAL 94.2%, GraCoRe 96.9%, NLGraph 98.4%).MA-GTS is open-sourced at https://github.com/ZIKEYUAN/MA-GTS.git.

翻译：图论问题广泛存在于物流配送、通信网络、交通优化等现实世界应用中。这些问题通常具有复杂性、噪声性和不规则性，对传统算法构成了挑战。大语言模型（LLMs）虽提供了潜在解决方案，但仍面临精度有限和输入长度受限等挑战。为应对这些挑战，我们提出了MA-GTS（多智能体图论求解器），这是一个通过智能体协作分解复杂问题的多智能体框架。MA-GTS将隐式表达的文本图数据映射为清晰的结构化图表示，并根据问题约束与图结构规模动态选择最合适的算法。该方法确保求解过程保持高效，且生成的推理路径具备可解释性。我们使用自行构建的现实世界启发式图论数据集G-REAL对MA-GTS进行验证。实验结果表明，MA-GTS在效率、精度和可扩展性方面均优于现有先进方法，在多个基准测试中取得优异结果（G-REAL 94.2%、GraCoRe 96.9%、NLGraph 98.4%）。MA-GTS已在https://github.com/ZIKEYUAN/MA-GTS.git开源。