The intersection graphs of subtrees in trees are exactly the chordal graphs

摘要: The intersection graph of a family subtrees in an undirected tree is called subtree graph. A chordal if every simple circuit with more than three vertices has edge connecting two non-consecutive vertices. In this paper, we prove that, for G, the following conditions are equivalent: (i) G graph; (ii) (iii) proper graph. Consider G. We give efficient algorithm constructing representation by tree.