The colored edge theory of A. Bulatov and binary absorption in minimal Taylor algebras
Zarathustra Brady, Petar {\DJ}api\'c, Petar Markovi\'c, Aleksandar Proki\'c, Vlado Uljarevi\'c
TL;DR
This paper introduces a new definition of colored edge graphs for minimal Taylor algebras, simplifying Bulatov's existing theory and extending it with clearer insights.
Contribution
It provides a novel, simplified framework for understanding Bulatov's colored edge graphs specifically for minimal Taylor algebras.
Findings
Reproves Bulatov's main results within the minimal Taylor algebra context
Introduces a new, inclusive definition of colored edge graphs for these algebras
Simplifies the theoretical framework compared to the general case
Abstract
We find a new definition of colored edge graphs of finite algebras in the case of minimal Taylor algebras, a definition which includes the graphs invented by A. Bulatov. Next we proceed to reprove the main results of A. Bulatov's theory in the case of minimal Taylor algebras and in our setting, finding several simplifications compared to the more general case of smooth algebras Bulatov considered.
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