Dichotomy for Digraph Homomorphism Problems
Abstract
We consider the problem of finding a homomorphism from an input digraph G to a fixed digraph H. We show that if H admits a weak-near-unanimity polymorphism φ then deciding whether G admits a homomorphism to H (HOM(H)) is polynomial time solvable? This gives a proof of the dichotomy conjecture (now dichotomy theorem) by Feder and Vardi [29]. Our approach is combinatorial, and it is simpler than the two algorithms found by Bulatov [9] and Zhuk [46] in 2017. We have implemented our algorithm and show some experimental results.
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