TITLE: Are all $4$-regular graphs Hamiltonian
QUESTION [12 upvotes]: It is easy to show that all connected $2$-regular graphs are Hamiltonian. The Petersen graph is a $3$-regular graph that is not Hamiltonian. 
Are there any $4$ regular graphs that are not Hamiltonian?
Thank you

REPLY [5 votes]: However, Tutte proved that a 4-connected planar graph is Hamiltonian.