The d -to- 1 conjecture of Khot asserts that it is hard to satisfy an fraction of constraints of a satisfiable d -to- 1 Label Cover instance, for arbitrarily small 0"> 0 . We prove that the d -to- 1 conjecture for any fixed d implies the hardness of coloring a 4 -colorable graph with C colors for arbitrarily large integers C . Earlier, this implication was only known under the 2 -to- 1 conjecture, which is the strongest in the family of d -to- 1 conjectures.