Asteroidal number: различия между версиями
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Graphs with '''asteroidal number''' at most two are commonly known as '''AT-free graphs'''. The | 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 graph|interval]], [[permutation graph|permutation]]'' and ''[[cocomparability graph|cocomparability]]'' graphs. | class of AT-free graphs contains well-known graph classes such as ''[[interval graph|interval]], [[permutation graph|permutation]]'' and ''[[cocomparability graph|cocomparability]]'' graphs. | ||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 16:12, 19 декабря 2011
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.
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.