2018/10/07 by Miroslav Olšák, Olšák, Miroslav
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #Data Management and Algorithms #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1810.03177
openalex publication_date 2018/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the existence of a term s satisfying s(r,a,r,e) = s(a,r,e,a) in a general algebraic structure is equivalent to an existence of a term t satisfying t(x,x,y,y,z,z)=t(y,z,z,x,x,y). As a consequence of a general version of this theorem and previous results we get that each strongly connected digraph of algebraic length one, which is compatible with an operation t satisfying an identity of the from t(…)=t(…), has a loop.