  Let $B$ and $R$ be two simple graphs with vertex set $V$, and let $G(B,R)$ be
the simple graph with vertex set $V$, in which two vertices are adjacent if
they are adjacent in at least one of $B$ and $R$. For $X \subseteq V$, we
denote by $B|X$ the subgraph of $B$ induced by $X$; let $R|X$ and $G(B,R)|X$ be
defined similarly. We say that the pair $(B,R)$ is {\em additive} if for every
$X \subseteq V$, the sum of the clique numbers of $B|X$ and $R|X$ is at least
the clique number of $G(B,R)|X$. In this paper we give a necessary and
sufficient characterization of additive pairs of graphs. This is a numerical
variant of a structural question studied in \cite{ABC}.
