Embodiments include methods, for an intermediate node in a wireless mesh network, to identify a critical link in a path between a source node and a destination node in the wireless mesh network. Such methods include receiving a first message relating to a discovery of a path between the source node and the destination node. Such methods also include forwarding the first message to one or more other nodes in the wireless mesh network based on an entry in a discovery table, stored in the intermediate node, that indicates that the intermediate node is part of a critical link in the path. The first message can be a path request message or a path reply message, and the methods can include various other operations associated with each type of first message. Other embodiments include wireless devices configured to operate as intermediate nodes in accordance with these methods.