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:

Comparing universal covers in polynomial time.

Fiala, J. and Paulusma, Daniel (2010) 'Comparing universal covers in polynomial time.', Theory of computing systems., 46 (4). pp. 620-635.


The universal cover T G of a connected graph G is the unique (possibly infinite) tree covering G, i.e., that allows a locally bijective homomorphism from T G to G. It is well-known that if a graph G covers a graph H, then their universal covers are isomorphic, and that the latter can be tested in polynomial time by checking if G and H share the same degree refinement matrix. We extend this result to locally injective and locally surjective homomorphisms by following a very different approach. Using linear programming techniques we design two polynomial time algorithms that check if there exists a locally injective or a locally surjective homomorphism, respectively, from a universal cover T G to a universal cover T H (both given by their degree matrices). This way we obtain two heuristics for testing the corresponding locally constrained graph homomorphisms. Our algorithm can also be used for testing (subgraph) isomorphism between universal covers, and for checking if there exists a locally injective or locally surjective homomorphism (role assignment) from a given tree to an arbitrary graph H.

Item Type:Article
Keywords:Graph homomorphism, Universal cover, Computational complexity, Degree matrix.
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:07 October 2010
Date of first online publication:May 2010
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar