Comparing universal covers in polynomial time

Fiala, J.; Paulusma., D.

doi:10.1007/s00224-009-9200-z

Comparing universal covers in polynomial time

Fiala, J.; Paulusma., D.

Authors

J. Fiala

Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor

Abstract

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.

Citation

Fiala, J., & Paulusma., D. (2010). Comparing universal covers in polynomial time. Theory of Computing Systems, 46(4), 620-635. https://doi.org/10.1007/s00224-009-9200-z

Journal Article Type	Article
Publication Date	May 1, 2010
Deposit Date	Oct 6, 2010
Publicly Available Date	Oct 7, 2010
Journal	Theory of Computing Systems
Print ISSN	1432-4350
Electronic ISSN	1433-0490
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	46
Issue	4
Pages	620-635
DOI	https://doi.org/10.1007/s00224-009-9200-z
Keywords	Graph homomorphism, Universal cover, Computational complexity, Degree matrix.
Public URL	https://durham-repository.worktribe.com/output/1548410