𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Quantifier-eliminable locally finite graphs

✍ Scribed by Shawn Hedman; Wai Yan Pong

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
79 KB
Volume
57
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

We identify the locally finite graphs that are quantifier-eliminable and their first order theories in the signature of distance predicates.

πŸ“œ SIMILAR VOLUMES

Finite Separating Sets in Locally Finite
Finite Separating Sets in Locally Finite Graphs
✍ H.A. Jung; M.E. Watkins πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 386 KB

An \((m, n)\)-separator of an infinite graph \(\Gamma\) is a smallest finite set of vertices whose deletion leaves at least \(m\) finite components and at least \(n\) infinite components. It is shown that a vertex of \(\Gamma\) of finite valence belongs to only finitely many \((0,2)\)-separators. Va

On bounded automorphisms of locally fini
On bounded automorphisms of locally finite transitive graphs
✍ Niemeyer, Peter πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 517 KB

The automorphism-group of an infinite graph acts in a natural way on the set of d-fibers (components of the set of rays with respect to the Hausdorff metric). For connected, locally finite, almost transitive graphs the kernel of this action is proved to be the group of bounded automorphisms. This co

On the hamiltonicity of line graphs of l
On the hamiltonicity of line graphs of locally finite, 6-edge-connected graphs
✍ Richard C. Brewster; Daryl Funk πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 124 KB

## Abstract The topological approach to the study of infinite graphs of Diestel and KÜhn has enabled several results on Hamilton cycles in finite graphs to be extended to locally finite graphs. We consider the result that the line graph of a finite 4‐edge‐connected graph is hamiltonian. We prove a

Cycle-cocycle partitions and faithful cy
Cycle-cocycle partitions and faithful cycle covers for locally finite graphs
✍ Henning Bruhn; Reinhard Diestel; Maya Stein πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 112 KB

## Abstract By a result of Gallai, every finite graph __G__ has a vertex partition into two parts each inducing an element of its cycle space. This fails for infinite graphs if, as usual, the cycle space is defined as the span of the edge sets of finite cycles in __G__. However, we show that, for t