An asteroidal triple is an independent set of three vertices in a graph such that every two of them are joined by a path avoiding the closed neighborhood of the third. Graphs without asteroidal triples are called AT-free graphs. The new suggested ordering generalizes the cocomparability ordering achievable for cocomparability graphs.
G is a cocomparability graph.
1997 Doc 1 cient algorithms in cocomparability and trapezoid graphs - Arvind, Breu et al. Doc 1 the powers of graphs with bounded asteroidal number - Ho, Chang et al.