# Hamiltonian and Eulerian cycles

Let $G=(V,E)$ be a graph that can be partitioned into Hamiltonian cycles. Show that there is a Eulerian cycle in $G$.

My intuition: I need help with the proof (I'm not sure my intuition is right) taking the union of all the subsets gives us a Hamiltonian cycle in $G$ Hamiltonian cycle has no repetitions when it comes to vertices then if there are no repetitions it means that there is no repetition when it comes to the edges either which means there has to be a Eulerian cycle by defintion.

• @user21312 Essentially you just stitch the Hamiltonian cycles that are given as partitioning $G$ together so you get one cycle. The stitching can be done at any vertex. – Parcly Taxel Mar 18 '17 at 12:15