# Up to a double cover, every regular connected graph is isomorphic to a Schreier graph

@article{Leemann2020UpTA, title={Up to a double cover, every regular connected graph is isomorphic to a Schreier graph}, author={P. Leemann}, journal={arXiv: Combinatorics}, year={2020} }

We prove that every connected locally finite regular graph has a double cover which is isomorphic to a Schreier graph.

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#### References

SHOWING 1-10 OF 10 REFERENCES

Every connected regular graph of even degree is a Schreier coset graph

- Mathematics, Computer Science
- J. Comb. Theory, Ser. B
- 1977

Using Petersen's theorem, that every regular graph of even degree is 2-factorable, it is proved that every connected regular graph is isomorphic to a Schreier coset graph. Expand

König's Duality Theorem for Infinite Bipartite Graphs

- Mathematics
- 1984

Dans tout graphe biparti il existe un couplage N et un recouvrement P tel que P consiste en un choix de 1 sommet a partir d'une arete dans N

Schreir graphs: Transitivity and coverings

- Computer Science, Mathematics
- Int. J. Algebra Comput.
- 2016

A characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems allows us to give a transitivity criterion for Schreiers graphs and shows that Tarski monsters satisfy a strong simplicity criterion. Expand

Algebraic Graph Theory

- Mathematics, Computer Science
- Graduate texts in mathematics
- 2001

The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial. Expand

Every finite non-solvable group admits an oriented regular representation

- Mathematics, Computer Science
- J. Comb. Theory, Ser. B
- 2017

It is shown that every finite non-solvable group admits an ORR, and a tool is provided that may prove useful in showing that some families of finite solvable groups admit ORRs. Expand

Discrete groups, expanding graphs and invariant measures

- Mathematics, Computer Science
- Progress in mathematics
- 1994

The Banach-Ruziewicz Problem for n = 2, 3 Ramanujan Graphs is solved and the representation theory of PGL 2 is explained. Expand

of Group Actions on Rooted Trees

- Mathematics
- 2016

We prove a general result about the decomposition into ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components… Expand

On subgroups and Schreier graphs of finitely generated groups

- Art
- 2016

Le sujet de cette these est la theorie geometrique et combinatoire des groupes - le lien entre les proprietes des groupes et celles des objets geometriques sur lesquels ils agissent. Plus… Expand

The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps

- Mathematics
- 2004

Algebraic graph theory, volume 207 of Graduate Texts in Mathematics

- 2001