  We show that for any unambiguous finite automaton with $n$ states there
exists an unambiguous finite automaton with $\sqrt{n+1} \cdot 2^{n/2}$ states
that recognizes the complement language. This builds and improves upon a
similar result by Jir\'asek et al. [Int. J. Found. Comput. Sci. 29 (5) (2018)].
Our improvement is based on a reduction to and an analysis of a problem from
extremal graph theory: we show that for any graph with $n$ vertices, the
product of the number of its cliques with the number of its cocliques
(independent sets) is bounded by $(n+1) 2^n$.
