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A k-hop dominating set is a subset of nodes such that each node that is not in the set can be reached within k hops from at least one node in the set. A connected k-hop dominating set can be used for disseminating topology update packets or route request packets, in which the flooding search space is reduced to the set, resulting in significant flooding overhead reduction in broadcast-related applications. In mobile ad hoc networks, a connected k-hop dominating set may become disconnected due to node mobility or switch-off, which necessitates the reformation of the k-hop dominating set. In this paper, we identify a sufficient condition that guarantees the connectivity of the virtual backbone. The condition can be verified in a distributed manner by the node only having the link information of its neighbors. (Unless specified otherwise, the term "neighbor" denotes a "1-hop neighbor." The link information of neighbors can be obtained by 2-hop neighbor information or 1-hop neighbor positions.) With the help of this condition, we propose a distributed algorithm for efficiently constructing and maintaining connected k-hop dominating sets in mobile ad hoc networks. Simulations show that our connected k-hop dominating set is small and stable and needs little maintenance overhead in the random-walk mobility and Gauss-Markov mobility models.