• Corpus ID: 222310779

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={Paul-Henry Leemann},
  journal={arXiv: Combinatorics},
  year={2020}
}
  • P. Leemann
  • Published 13 October 2020
  • Mathematics
  • arXiv: Combinatorics
We prove that every connected locally finite regular graph has a double cover which is isomorphic to a Schreier graph. 

Figures from this paper

Integrable and Chaotic Systems Associated with Fractal Groups

This paper provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, and contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

References

SHOWING 1-10 OF 13 REFERENCES

Presentations for vertex-transitive graphs

We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation

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

  • J. Gross
  • Mathematics, Computer Science
    J. Comb. Theory, Ser. B
  • 1977

König's Duality Theorem for Infinite Bipartite Graphs

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

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.

Algebraic Graph Theory

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

Discrete groups, expanding graphs and invariant measures

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

Infinite digraphs with given regular automorphism groups

  • L. Babai
  • Mathematics
    J. Comb. Theory, Ser. B
  • 1978

On a class of fixed-point-free graphs

A number of papers [1; 2; 3; 4] have dealt with the construction of nnite graphs X whose automorphism group G(X) is isomorphic to a given finite group G. Examination of the graphs constructed in

of Group Actions on Rooted Trees

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

On subgroups and Schreier graphs of finitely generated groups

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