Asteroidal Triple of Edges in Bichordal Graphs: A Complete list

Three independent vertices in a graph form an asteroidal triple (AT) if for any two of them, there is a path that avoids the neighbours of the third vertex. The motivation to work on this topic came from the study of interval graphs. A graph is an interval graph if its vertices can be put in a one-to-one correspondence with a family of intervals on the real line in such a way that two vertices are adjacent if and only if the corresponding intervals intersect. Lekkerkerker and Boland [5] proved that a graph is an interval graph if and only if it is chordal and AT-free. Corneil, Olariu and Stewart [1] have done excellent and extensive work on asteroidal triples.