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Type: Artigo de periódico
Title: Algebraic theory for the clique operator
Author: Gutierrez, Marisa
Meidanis, João
Abstract: 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.
Subject: Helly graphs
intersection graphs
Editor: Sociedade Brasileira de Computação
Rights: aberto
Identifier DOI: 10.1590/S0104-65002001000200008
Date Issue: 1-Jan-2001
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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