The problem of enumerating connected subgraphs of a given size in a graph has been extensively studied in recent years. In this short communication, we propose an algorithm with a delay of $\mathcal{O}(k\Delta)$ for enumerating all connected induced subgraphs of size $k$ in an undirected graph $G=(V, E)$, where $k$ and $\Delta$ are respectively the size of subgraphs and the maximum degree of $G$. The proposed algorithm improves upon the current best delay bound $\mathcal{O}(k^2\Delta)$ for the connected induced subgraph enumeration problem in the literature.

翻译：近年来，图中给定大小的连通子图枚举问题受到了广泛研究。在本文短讯中，我们提出了一种时延为 $\mathcal{O}(k\Delta)$ 的算法，用于枚举无向图 $G=(V, E)$ 中所有大小为 $k$ 的连通导出子图，其中 $k$ 和 $\Delta$ 分别表示子图大小和 $G$ 的最大度数。该算法改进了现有文献中针对连通导出子图枚举问题的最优时延界 $\mathcal{O}(k^2\Delta)$。