# Computational Complexity of Covering Two-vertex Multigraphs with Semi-edges

@article{Bok2021ComputationalCO, title={Computational Complexity of Covering Two-vertex Multigraphs with Semi-edges}, author={Jan Bok and Jir{\'i} Fiala and Petr Hliněn{\'y} and Nikola Jedli{\vc}kov{\'a} and Jan Kratochv{\'i}l}, journal={ArXiv}, year={2021}, volume={abs/2103.15214} }

We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for graphs with semi-edges. The notion of graph covering is a discretization of coverings between surfaces or topological spaces, a notion well known and deeply studied in classical topology. Graph covers have found applications in discrete mathematics for constructing highly symmetric graphs, and in computer science in the theory of local computations. In 1991, Abello et al. asked…

## Figures from this paper

## One Citation

An Algorithmic Framework for Locally Constrained Homomorphisms

- MathematicsArXiv
- 2022

A homomorphism f from a guest graph G to a host graph H is locally bijective, injective or surjective if for every u ∈ V (G), the restriction of f to the neighbourhood of u is bijective, injective or…

## References

SHOWING 1-10 OF 47 REFERENCES

Revisiting Leighton’s theorem with the Haar measure

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2020

Abstract Leighton’s graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton’s theorem that allows…

The Power and the Limitations of Local Computations on Graphs

- Mathematics, Computer ScienceWG
- 1992

This paper uses local computations to define a notion of graph recognition, in particular the model enables a simulation of finite automata on words and on trees and introduces the notion of k-covering to examine limitations of such systems.

Generalized H-Coloring of Graphs

- MathematicsISAAC
- 2000

For fixed simple graph H and subsets of natural numbers σ and ρ, (H, σ, ρ)-colorings are introduced as generalizations of H-colorings of graphs and the study of how these colorings are related is initiated.

Generating all graph coverings by permutation voltage assignments

- MathematicsDiscret. Math.
- 1977

Graph labelings derived from models in distributed computing: A complete complexity classification

- Mathematics, Computer ScienceNetworks
- 2011

The computational complexity of the decision problems if the leader election and if the naming problem can be solved on a given network is settled by translating each problem into a graph labeling problem and obtaining an alternative proof for the already known co‐NP‐completeness result.