We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Finding vertex-surjective graph homomorphisms.

Golovach, P.A. and Lidicky, B. and Martin, B. and Paulusma, Daniel (2012) 'Finding vertex-surjective graph homomorphisms.', Acta informatica., 49 (6). pp. 381-394.


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:Article
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher statement:The original publication is available at
Date accepted:No date available
Date deposited:17 April 2013
Date of first online publication:September 2012
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar