The Complexity of Surjective Homomorphism Problems -- a Survey

Manuel Bodirsky (1) , Barnaby Martin (1) , Jan Kara

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems, surjective homomorphism problems seem to be harder to classify and we examine especially three concrete problems that have arisen from the literature, two of which remain of open complexity.

Domaines: Complexité [cs.CC]; Mathématique discrète [cs.DM]

Manuel Bodirsky, Barnaby Martin, Jan Kara. The Complexity of Surjective Homomorphism Problems -- a Survey. Discrete Applied Mathematics, 2012, 160 (12), pp.1680-1690. ⟨10.1016/j.dam.2012.03.029⟩. ⟨hal-00756923⟩