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Journal of the Brazilian Computer Society

Print version ISSN 0104-6500On-line version ISSN 1678-4804

Abstract

GUTIERREZ, Marisa  and  MEIDANIS, João. Algebraic theory for the clique operator. J. Braz. Comp. Soc. [online]. 2001, vol.7, n.3, pp.53-64. ISSN 0104-6500.  http://dx.doi.org/10.1590/S0104-65002001000200008.

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.

Keywords : Helly graphs; intersection graphs.

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