Algebraic theory for the clique operator

• Autor(a) principal: Gutierrez,Marisa
• Data de Publicação: 2001
• Outros Autores: Meidanis,João
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Journal of the Brazilian Computer Society
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002001000200008
• topic: Helly graphs; intersection graphs

In this text we attempt to unify many results about the K operator based on a new theory involving graphs, families and operators. We are able to build an ''operator algebra'' that helps to unify and automate arguments. In addition, we relate well-known properties, such as the Helly property, to the families and the operators. As a result, we deduce many classic results in clique graph theory from the basic fact that CS = I for conformal, reduced families. This includes Hamelink's construction, Roberts and Spencer theorem, and Ban-delt and Prisner's partial characterization of clique-fixed classes [2]. Furthermore, we show the power of our approach proving general results that lead to polynomial recognition of certain graph classes.