We present the on-demand link vector (OLIVE) protocol, a routing protocol for ad-hoc networks based on link-state information that is free of routing loops and supports destination-based packet forwarding. Routers exchange routing information reactively for each destination in the form of complete paths, and each node creates a labeled source graph based on the paths advertised by its neighbors. A node originates a broadcast route request to obtain a route for a destination for which a complete path does not exist in its source graph. When the original path breaks, a node can select an alternative path based on information reported by neighbors, and a node can send a unicast route request to verify that the route is still active. A node that cannot find any alternate path to a destination sends route errors reliably to those neighbors that were using it as next hop to the destination. Using simulation experiments in ns2, OLIVE is shown to outperform DSR, AODV, OLSR and TBRPF, in terms of control overhead, throughput, and average network delay, while maintaining loop-free routing with no need for source routes.