Algebra universalis

, 79:31 | Cite as

Unique inclusions of maximal C-clones in maximal clones

  • Mike BehrischEmail author
  • Edith Vargas-García
Open Access


C-clones are polymorphism sets of so-called clausal relations, a special type of relations on a finite domain, which first appeared in connection with constraint satisfaction problems in work by Creignou et al. from 2008. We completely describe the relationship regarding set inclusion between maximal C-clones and maximal clones. As a main result we obtain that for every maximal C-clone there exists exactly one maximal clone in which it is contained. A precise description of this unique maximal clone, as well as a corresponding completeness criterion for C-clones is given.


Clone C-clone Clausal relation Maximal C-clone Maximal clone 

Mathematics Subject Classification

08A40 08A02 08A99 



Open access funding provided by TU Wien (TUW).


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Authors and Affiliations

  1. 1.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienViennaAustria
  2. 2.Instituto Tecnológico Autónomo de MéxicoMexicoMexico

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