Keywords:
				
				
																		Uniquely Hamiltonian, 													Infinite Hamilton cycle, 													Cubic graph															
			
			
										
					
Abstract
					Investigating a problem of B. Mohar, we show that every one-ended Hamiltonian cubic graph with end degree 3 contains a second Hamilton cycle. We also construct two examples showing that this result does not extend to give a third Hamilton cycle, nor that it extends to the two-ended case.