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On the representation of triangulation graphs in trees. (English) Zbl 0541.05049
A graph G is said to be tree-representable if there exist a tree T and a family $$T_ i$$ ($$i\in I)$$ of subtrees of T such that G is isomorphic to the intersection graph of this family. It has been shown independently by several authors that if G is a finite graph then G is tree-representable if and only if G is chordal, i.e., no cycle of length at least 4 is an induced subgraph of G. It is not true that every infinite chordal graph is tree-representable. The author’s main result is a characterization of all tree-representable graphs, given by means of simplicial decompositions.
Reviewer: L.Lesniak

##### MSC:
 05C75 Structural characterization of families of graphs 05C05 Trees
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