Silicon-carbon alloy structures can be formed as inverted U-shaped structures around semiconductor fins by a selective epitaxy process. A planarization dielectric layer is formed to fill gaps among the silicon-carbon alloy structures. After planarization, remaining vertical portions of the silicon-carbon alloy structures constitute silicon-carbon alloy fins, which can have sublithographic widths. The semiconductor fins may be replaced with replacement dielectric material fins. In one embodiment, employing a patterned mask layer, sidewalls of the silicon-carbon alloy fins can be removed around end portions of each silicon-carbon alloy fin. An anneal is performed to covert surface portions of the silicon-carbon alloy fins into graphene layers. In one embodiment, each graphene layer can include only a horizontal portion in a channel region, and include a horizontal portion and sidewall portions in source and drain regions. If a patterned mask layer is not employed, each graphene layer can include only a horizontal portion.