Dichotomy for Digraph Homomorphism Problems

@article{Rafiey2017DichotomyFD,
  title={Dichotomy for Digraph Homomorphism Problems},
  author={Arash Rafiey and Jeff Kinne and Tom{\'a}s Feder},
  journal={CoRR},
  year={2017},
  volume={abs/1701.02409}
}
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 confirms the conjecture of Bulatov, Jeavons, and Krokhin [BJK05], in the form postulated by Maroti and McKenzie [MM08], and consequently implies the validity of the celebrated dichotomy conjecture due to Feder and Vardi [FV93]. We transform the… CONTINUE READING
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