In this paper we consider the problem of listing the maximal k-degenerate induced subgraphs of a chordal graph, and propose an output-sensitive algorithm using delay $O(m\cdot \omega (G))$ for any n-vertex chordal graph with m edges, where $\omega (G)\le n$ is the maximum size of a clique in G. Degeneracy is a well known sparsity measure, and k-degenerate subgraphs are a notion of sparse subgraphs, which generalizes other problems such as independent sets (0-degenerate subgraphs) and forests (1-degenerate subgraphs).

Many efficient enumeration algorithms are designed by solving the so-called Extension problem, which asks whether there exists a maximal solution containing a given set of nodes, but no node from a forbidden set. We show that solving this problem is np-complete for maximal k-degenerate induced subgraphs, motivating the need for additional techniques.

在本文中，我们考虑列出一个弦图的最大k个退化的诱导子图的问题，并提出一种使用时延的输出敏感算法$Ø（米\cdot \omega （G））$对于任何具有m个边的n-顶点弦和弦图，其中$\omega （G）\le ñ$是G中的集团的最大大小。退化是众所周知的稀疏性度量，k退化子图是稀疏子图的概念，它泛化了其他问题，例如独立集（0退化子图）和森林（1退化子图）。

通过解决所谓的扩展问题，设计了许多有效的枚举算法，该问题询问是否存在包含给定节点集但不包含禁止集中的节点的最大解。我们表明，解决这个问题是NP -完全的最大ķ -degenerate诱导子图，激励更多的技术的需要。