# Finding vertex-surjective graph homomorphisms

Golovach, Petr A., Lidický, Bernard, Martin, Barnaby and Paulusma, Daniël
(2012)
*Finding vertex-surjective graph homomorphisms.*
In: 7th International Computer Science Symposium (CSR 2012), 3-7 Jul 2012, Nizhny Novgorod, Russia.
(doi:10.1007/978-3-642-30642-6_16)

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## Abstract

The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can be formulated in terms of spanning subgraphs and subgraphs, and as such their computational complexity has been extensively studied. What about the surjective variant? Because this problem is NP-complete in general, we restrict the guest and the host graph to belong to graph classes G and H, respectively. We determine to what extent a certain choice of G and H influences its computational complexity. We observe that the problem is polynomial-time solvable if H is the class of paths, whereas it is NP-complete if G is the class of paths. Moreover, we show that the problem is even NP-complete on many other elementary graph classes, namely linear forests, unions of complete graphs, cographs, proper interval graphs, split graphs and trees of pathwidth at most 2. In contrast, we prove that the problem is fixed-parameter tractable in k if G is the class of trees and H is the class of trees with at most k leaves, or if G and H are equal to the class of graphs with vertex cover number at most k.

Item Type: | Conference or Workshop Item (Paper) |
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Additional Information: | Golovach P.A., Lidický B., Martin B., Paulusma D. (2012) Finding Vertex-Surjective Graph Homomorphisms. In: Hirsch E.A., Karhumäki J., Lepistö A., Prilutskii M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg |

Research Areas: | A. > School of Science and Technology > Computer Science A. > School of Science and Technology > Computer Science > Foundations of Computing group |

Item ID: | 9655 |

Useful Links: | |

Depositing User: | Devika Mohan |

Date Deposited: | 20 Dec 2012 11:19 |

Last Modified: | 24 Apr 2018 13:53 |

ISBN: | 9783642306419 |

URI: | https://eprints.mdx.ac.uk/id/eprint/9655 |

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