Eulerian and Hamiltonian Graphs · Challenge problem

Split $6$ people into two groups of three, $L=\{1,2,3\}$ and $R=\{4,5,6\}$, with everyone in $L$ friends with everyone in $R$ and no other friendships — $K_{3,3}$, which does have Hamiltonian cycles (for example $1,4,2,5,3,6$ and back to $1$). What is the minimum number of people who must leave the group so that NO circular seating of the remaining people has every neighbor pair friends?