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'''Clique-transversal''' --- кликовая трансверсаль.  
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'''Clique-transversal''' — ''[[кликовая трансверсаль]].''
  
A '''clique-transversal''' of a graph <math>G</math> is a subset of vertices that
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A '''clique-transversal''' of a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> is a subset of [[vertex|vertices]] that meets all the [[clique|cliques]]. A '''clique-independent set''' is a collection of pairwise vertex disjoint cliques. The '''[[clique-transversal number]]''' and '''[[clique-independence number]]''' of <math>\,G</math>, denoted by <math>\,\tau_{c}(G)</math> and <math>\,\alpha_{c}(G)</math>, are the sizes of a
meets all the cliques. A '''clique-independent set''' is a collection
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minimum clique-transversal and a maximum [[clique-independent set]] of <math>\,G</math>,
of pairwise vertex disjoint cliques. The '''clique-transversal number''' and '''clique-independence number''' of <math>G</math>, denoted by
 
<math>\tau_{c}(G)</math> and <math>\alpha_{c}(G)</math>, are the sizes of a
 
minimum clique-transversal and a maximum clique-independent set of <math>G</math>,
 
 
respectively.
 
respectively.
  
It is easy to see that <math>\tau_{c}(G) \geq \alpha_{c}(G)</math> for any graph
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It is easy to see that <math>\tau_{c}(G) \geq \alpha_{c}(G)</math> for any graph <math>\,G</math>. A graph <math>\,G</math> is '''[[clique-perfect graph|clique-perfect]]''' if <math>\,\tau_{c}(H) =
<math>G</math>. A graph <math>G</math> is '''clique-perfect''' if <math>\tau_{c}(H) =
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\alpha_{c}(H)</math> for every induced [[subgraph]] <math>\,H</math> of <math>\,G</math>. If this equality holds for the graph <math>\,G</math>, we say that <math>\,G</math> is '''[[clique-good graph|clique-good]]'''.
\alpha_{c}(H)</math> for every induced subgraph <math>H</math> of <math>G</math>. If this equality
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holds for the graph <math>G</math>, we say that <math>G</math> is '''clique-good'''.
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==Литература==
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* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.

Текущая версия на 12:03, 11 ноября 2013

Clique-transversalкликовая трансверсаль.

A clique-transversal of a graph \,G is a subset of vertices that meets all the cliques. A clique-independent set is a collection of pairwise vertex disjoint cliques. The clique-transversal number and clique-independence number of \,G, denoted by \,\tau_{c}(G) and \,\alpha_{c}(G), are the sizes of a minimum clique-transversal and a maximum clique-independent set of \,G, respectively.

It is easy to see that \tau_{c}(G) \geq \alpha_{c}(G) for any graph \,G. A graph \,G is clique-perfect if \,\tau_{c}(H) =
\alpha_{c}(H) for every induced subgraph \,H of \,G. If this equality holds for the graph \,G, we say that \,G is clique-good.

Литература

  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.