# Clique covering number vs. number of maximal cliques

Given a simple oriented graph $$G$$, let $$\theta(G)$$ be the clique covering number of G (i.e. the minimum number of cliques needed to cover the vertices of G) and $$m(G)$$ be the number of maximal cliques of $$G$$. For example, for the 5-cycle $$C_5$$, $$\theta(C_5) = 3$$ and $$m(C_5) = 5$$ (since there are 5 2-cliques).

Given a graph G, why does $$\theta(G) \leq m(G)$$ ? (equality for every induced graph is the definition of trivially perfect graphs).

Should be trivial, but I'm missing something.

Every vertex belongs to a maximal clique. By taking the set of all maximal cliques you cover all the vertices (e.g. all $$2$$-cliques from your example), so $$m(G)\geq\theta(G)$$.