Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. However, for many applications, it is desirable that the found subgraph has as few connections to the rest of the graph as possible, which gives rise to the Secluded Π-Subgraph problem. Here, input k is the size of the desired subgraph, and input t is a limit on the number of neighbors this subgraph has in the rest of the graph. This problem has been studied from a parameterized perspective, and unfortunately it turns out to be W[1]-hard for many graph properties Π, even when parameterized by $k+t$. We show that the situation changes when we are looking for a connected induced subgraph satisfying Π. In particular, we show that the Connected Secluded Π-Subgraph problem is FPT when parameterized by just t for many important graph properties Π.

与查找满足给定属性的诱导子图有关的问题构成了图算法中研究最多的领域之一。然而，对于许多应用，希望的是，发现有子，以图成为可能，这引起了其余几个连接僻静Π-子图问题。在此，输入k是所需子图的大小，输入t是对该子图在其余图中具有的邻居数的限制。从参数化的角度研究了这个问题，不幸的是，即使通过$ķ+Ť$。我们发现当寻找满足Π的连通诱导子图时，情况发生了变化。特别是，我们表明，连接僻静Π -Subgraph问题是FPT时只是参数牛逼了许多重要的图形属性Π。