Acessibilidade / Reportar erro

Algebraic theory for the clique operator

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.

Helly graphs; intersection graphs


Sociedade Brasileira de Computação Sociedade Brasileira de Computação - UFRGS, Av. Bento Gonçalves 9500, B. Agronomia, Caixa Postal 15064, 91501-970 Porto Alegre, RS - Brazil, Tel. / Fax: (55 51) 316.6835 - Campinas - SP - Brazil
E-mail: jbcs@icmc.sc.usp.br