In this paper, we consider the problems of enumerating minimal vertex covers and minimal dominating sets with capacity and/or connectivity constraints. We develop polynomial-delay enumeration algorithms for these problems on bounded-degree graphs. For the case of minimal connected vertex cover, our algorithm runs in polynomial delay even on the class of $d$-claw free graphs, which extends the result on bounded-degree graphs. To complement these algorithmic results, we show that the problems of enumerating minimal connected vertex covers and minimal capacitated vertex covers in bipartite graphs are at least as hard as enumerating minimal transversals in hypergraphs.

翻译：本文研究带容量和/或连通性约束的极小顶点覆盖与极小支配集的枚举问题。我们针对有界度图上的这些问题，提出了多项式延迟枚举算法。对于极小连通顶点覆盖的情形，我们的算法在$d$-无爪图类上仍具有多项式延迟，这扩展了有界度图上的结果。作为这些算法结果的补充，我们证明在二分图上枚举极小连通顶点覆盖与极小容量顶点覆盖的问题，至少与在超图中枚举极小横向问题具有相同的难度。