NMC 2008 Problem 2

Assume that $n \geq 3$ people with different names sit around a round table. We call any unordered pair of them, say $M$ and $N$, dominating, if

(i) $M$ and $N$ do not sit on adjacent seats, and

(ii) on one (or both) of the arcs connecting $M$ and $N$ along the table edge, all people have names that come alphabetically after the names of $M$ and $N$.

Determine the minimal number of dominating pairs.