Ray-like graphs

I.V. Protasov

We prove that a graph $\Gamma$ is coarsely equivalent to ray if and only if $\Gamma$ is uniformly spherically bounded. We introduce and study some other classes of graphs asymptotically close to ray.

1. Dranishnikov A Asymptotic topology, Russian Math. Surveys, 55,(2000), №6, 71-116.

2. Gromov M. Asymptotic invariants of infinite groups, London Math. Soc. Lecture Note Ser., 182 (1993).

3. Harpe P.Topics in Geomatrical Group Theory, University Chicago Press, 2000

4. Kuchaiev O., Tsvietkova A., Asymptotic rays, Algebra and Discrete Math. (submitted).

5. Protasov I., Banakh T., Ball structures and Colorings of Groups and Graphs, Math. Stud. Monogr. Ser. 11(2003).

6. Roe J. Lectures on Coarse Geometry, AMS University Lecture Ser., 31(2003)

	Ray-like graphs
Author	I.V. Protasov protasov@unicyb.kiev.ua Kyiv National University
Abstract	We prove that a graph $\Gamma$ is coarsely equivalent to ray if and only if $\Gamma$ is uniformly spherically bounded. We introduce and study some other classes of graphs asymptotically close to ray.
Keywords	graph, ray, coarse equivalence, asymptotically closeness to ray, uniformly sperically boundedness
DOI	doi:10.30970/ms.27.1.19-29
Reference	1. Dranishnikov A Asymptotic topology, Russian Math. Surveys, 55,(2000), №6, 71-116. 2. Gromov M. Asymptotic invariants of infinite groups, London Math. Soc. Lecture Note Ser., 182 (1993). 3. Harpe P.Topics in Geomatrical Group Theory, University Chicago Press, 2000 4. Kuchaiev O., Tsvietkova A., Asymptotic rays, Algebra and Discrete Math. (submitted). 5. Protasov I., Banakh T., Ball structures and Colorings of Groups and Graphs, Math. Stud. Monogr. Ser. 11(2003). 6. Roe J. Lectures on Coarse Geometry, AMS University Lecture Ser., 31(2003)
Pages	19-29
Volume	27
Issue	1
Year	2007
Journal	Matematychni Studii
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