Asteroidal number: различия между версиями

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'''Asteroidal number''' --- астероидальное число.  
'''Asteroidal number''' — ''[[астероидальное число]].''


A set of
A set of [[vertex|vertices]] <math>A \subseteq V</math> of a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G = (V,E)</math> is an '''asteroidal set''' if for each <math>a \in A</math> the set <math>\,A - a</math> is contained in one
vertices <math>A \subseteq V</math> of a graph <math>G = (V,E)</math> is an '''asteroidal set''' if for each <math>a \in A</math> the set <math>A - a</math> is contained in one
component of <math>\,G - N[a]</math>. The '''asteroidal number''' of a graph <math>\,G</math>, denoted by
component of <math>G - N[a]</math>. The '''asteroidal number''' of a graph <math>G</math>, denoted by
<math>\,an(G)</math>, is the maximum cardinality of the asteroidal set in <math>\,G</math>.
<math>an(G)</math>, is the maximum cardinality of the asteroidal set in <math>G</math>.


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, permutation'' and ''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 numberастероидальное 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.