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Power saving in the Internet has become important since different applications in the Internet are increasing tremendously, along with their power consumption. We propose a robust distributed routing protocol for power saving in wired core networks. The proposed protocol coordinates how core routers go into power saving mode without degrading quality of service and network connectivity during non-peak hours. It saves power if some core routers in a network are able to switch to power saving mode through installing the protocol. This protocol is designed to be built on top of any existing distributed routing protocols in the Internet without any compatibility problems. Numerical results showed that the protocol can save up to 47.5% of the power used in a core router, and up to 18% of the power consumption of the whole network.