Clique tree

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Clique treeкликовое дерево.

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


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