Clique tree

Clique tree --- кликовое дерево.

Suppose [math]\displaystyle{ G }[/math] is any graph and [math]\displaystyle{ T }[/math] is a tree whose vertices --- call them nodes to help avoid confusing them with the vertices of [math]\displaystyle{ G }[/math] --- are precisely the maxcliques of [math]\displaystyle{ G }[/math]. For every [math]\displaystyle{ v \in V(G) }[/math], let [math]\displaystyle{ T_{v} }[/math] denote a subgraph of [math]\displaystyle{ T }[/math] induced by those nodes that contain [math]\displaystyle{ v }[/math]. If every such [math]\displaystyle{ T_{v} }[/math] is connected --- in other words, if every [math]\displaystyle{ T_{v} }[/math] is a subtree of [math]\displaystyle{ T }[/math] --- then call [math]\displaystyle{ T }[/math] a clique tree for [math]\displaystyle{ G }[/math].