  Indeterminate strings have received considerable attention in the recent
past; see for example Christodoulakis et al 2015 and Helling et al 2017. This
attention is due to their applicability in bioinformatics, and to the natural
correspondence with undirected graphs. One aspect of this correspondence is the
fact that the minimal alphabet size of indeterminates representing any given
undirected graph corresponds to the size of the minimal clique cover of this
graph. This paper solves a related problem proposed in Helling et al 2017:
compute $\Theta_n(m)$, which is the size of the largest possible minimal clique
cover (i.e., an exact upper bound), and hence alphabet size of the
corresponding indeterminate, of any graph on $n$ vertices and $m$ edges.
