Asteroidal number

Asteroidal number — астероидальное число.

A set of vertices [math]\displaystyle{ A \subseteq V }[/math] of a graph [math]\displaystyle{ G = (V,E) }[/math] is an asteroidal set if for each [math]\displaystyle{ a \in A }[/math] the set [math]\displaystyle{ A - a }[/math] is contained in one component of [math]\displaystyle{ G - N[a] }[/math]. The asteroidal number of a graph [math]\displaystyle{ G }[/math], denoted by [math]\displaystyle{ an(G) }[/math], is the maximum cardinality of the asteroidal set in [math]\displaystyle{ G }[/math].

Graphs with asteroidal number at most two are commonly known as AT-free graphs. The class of AT-free graphs contains well-known graph classes such as interval, permutation and cocomparability graphs.