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 covers, our algorithms run in polynomial delay even on the class of $d$-claw free graphs, extending the result on bounded-degree graphs, and in output quasi-polynomial time on general graphs. To complement these algorithmic results, we show that the problems of enumerating minimal connected vertex covers, minimal connected dominating sets, and minimal capacitated vertex covers in $2$-degenerated bipartite graphs are at least as hard as enumerating minimal transversals in hypergraphs.

翻译：本文研究了枚举具有容量和/或连通性约束的最小顶点覆盖与最小支配集的问题。针对有界度图，我们为这些问题设计了多项式延迟枚举算法。对于最小连通顶点覆盖的情形，我们的算法甚至在$d$-无爪图类上也能以多项式延迟运行，从而将有界度图上的结果推广到更广的图类；在一般图上则能以输出拟多项式时间运行。作为这些算法结果的补充，我们证明了在$2$-退化二分图中枚举最小连通顶点覆盖、最小连通支配集以及最小容量顶点覆盖的问题，其难度至少与枚举超图中的最小横截集相当。