An asteroidal triple in a graph G is a set of three non-adjacent 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 AT-free graph. The class of AT-free graphs is a graph class for which many NP-complete problems are solvable in polynomial time. Amongst them, independent set and coloring.
Algorithms for asteroidal triples and asteroidal numbers in graphs.
Algorithms for asteroidal triples and asteroidal numbers in graphs.
An asteroidal triple in a graph G is a set of three non-adjacent 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 AT-free graph. The class of AT-free graphs is a graph class for which many NP-complete problems are solvable in polynomial time. Amongst them, independent set and coloring.
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them
