Hello Narad
An MPLS network relies on end to end label switched paths (LSPs) to be established across the network. If LSPs fail, then the MPLS network will fail. LSPs are maintained most often by using the LDP protocol.
However, it is possible to configure an MPLS network to use what is known as MPLS RSVP TE (Traffic Engineering). In such a setup, RSVP is used to set up label switched paths that can be used for TE in MPLS networks. More about this can be found in the following Cisco document:
It is possible to use another routing protocol within the MPLS core, or even to use static routing if you like. The important thing is to ensure that all core MPLS routers are reachable. OSPF is the routing protocol of choice however, especially for larger MPLS networks.
Take a look at this post:
I hope this has been helpful!
Laz