Tolerance intersection graphs on binary trees with constant tolerance 3 Original Research Article

A chordal graph is the intersection graph of a family of subtrees of a tree, or, equivalently, it is the (edge-)intersection graph of leaf-generated subtrees of a full binary tree. In this paper, a generalization of chordal graphs from this viewpoint is studied: a graph G=(V,E) is representable if there is a family of subtrees {Sv}v∈V of a binary tree, such that uv∈E if and only if |Su∩Sv|⩾3.