A method is provided in one example embodiment and includes receiving a label-mapping message at a first router. The first router does not record the label-mapping message. The method further includes sending the label mapping message toward a root router of a Multipoint Label Switched Path (MPLSP) in a network and, further, evaluating a path vector sent from the root router to identify whether a first router's address is part of the path vector. If the first router's address is present in the path vector then a label mapping associated with the path vector is not installed by the first router. In more detailed embodiments, the first router identifies that if the first router's address is part of the path vector, a loop is present in the network. If the first router's address is not part of the path vector, the label mapping associated with the path vector is recorded.