The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle. Within this paper, we present three integer linear programs specifically formulated to yield optimal solutions for this problem. The branch-and-cut algorithm has been used for two models. To demonstrate the computational efficiency of these methods, we utilize them on a range of real-world graphs as well as random graphs. Additionally, we conduct a comparative analysis against approaches previously proposed in the literature.

翻译：最长诱导（或弦环）环问题是一类被归类为NP完全的图论问题，其核心在于确定图中最大的顶点子集，使得由此诱导的子图构成一个环。本文提出了三种整数线性规划模型，专门用于获取该问题的最优解。其中两个模型采用了分支切割算法。为验证这些方法的计算效率，我们在多种真实图与随机图上进行了实验。此外，我们还与文献中先前提出的方法开展了对比分析。