Algebraic theory for the clique operator

Journal of the Brazilian Computer Society

Universidade Estadual de Campinas, Campinas, Brazil¹  Gutierrez, Marisa¹  Meidanis, João¹  Universidad Nacional de La Plata, La Plata, Argentina¹ 

关键词: Helly graphs;    intersection graphs;   

DOI  :  10.1590/S0104-65002001000200008

学科分类：农业科学（综合）

来源: Springer U K

【 摘 要 】

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.

【 授权许可】

Unknown