Structures and methods for forming a patterned graphene layer on a substrate. One such method includes forming at least one patterned structure of a carbide-forming metal or metal-containing alloy on a substrate, applying a layer of graphene on top of the at least one patterned structure of a carbide-forming metal or metal-containing alloy on the substrate, heating the layer of graphene on top of the at least one patterned structure of a carbide-forming metal or metal-containing alloy in an environment to remove graphene regions proximate to the at least one patterned structure of a carbide-forming metal or metal-containing alloy, and removing the at least one patterned structure of a carbide-forming metal or metal-containing alloy to produce a patterned graphene layer on the substrate, wherein the patterned graphene layer on the substrate provides carrier mobility for electronic devices.