Unique inclusions of maximal C-clones in maximal clones

Abstract

C-clones are polymorphism sets of so-called clausal relations, aspecial type of relations on a finite domain, which first appeared in con-nection with constraint satisfaction problems in work by Creignou et al.from2008. We completely describe the relationship regarding set inclu-sion between maximal C-clones and maximal clones. As a main result weobtain that for every maximal C-clone there exists exactly one maximalclone in which it is contained. A precise description of this unique maxi-mal clone, as well as a corresponding completeness criterion for C-clonesis given.