Eulerian and Hamiltonian Graphs · Medium problem

A double-five domino set has $21$ dominoes (all pairs $(i,j)$ with $0 \le i \le j \le 5$). Model this as a multigraph with vertices $0,\ldots,5$ and each domino as an edge. Each vertex initially has odd degree. What is the fewest dominoes that must be removed so that the remaining dominoes can be laid in a closed ring (forming an Euler circuit)?