Asteroidal#
Algorithms for asteroidal triples and asteroidal numbers in graphs.
An asteroidal triple in a graph G is a set of three nonadjacent vertices u, v and w such that there exist a path between any two of them that avoids closed neighborhood of the third. More formally, v_j, v_k belongs to the same connected component of G  N[v_i], where N[v_i] denotes the closed neighborhood of v_i. A graph which does not contain any asteroidal triples is called an ATfree graph. The class of ATfree graphs is a graph class for which many NPcomplete problems are solvable in polynomial time. Amongst them, independent set and coloring.

Check if a graph is ATfree. 
Find an asteroidal triple in the given graph. 