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Interactions between large-scale invariants in infinite graphs
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Federici, Bruno (2017) Interactions between large-scale invariants in infinite graphs. PhD thesis, University of Warwick.
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WRAP_Theses_Federici_2017.pdf - Submitted Version - Requires a PDF viewer. Download (1077Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3226902~S15
Abstract
This thesis is devoted to the study of a number of properties of graphs. Our first main result clarifies the relationship between hyperbolicity and non-amenability for plane graphs of bounded degree. This generalises a known result for Cayley graphs to bounded degree graphs. The second main result provides a counterexample to a conjecture of Benjamini asking whether a transient, hyperbolic graph must have a transient subtree. In Chapter 4 we endow the set of all graphs with two pseudometrics and we compare metric properties arising from each of them. The two remaining chapters deal with bi-infinite paths in Z² and geodetic Cayley graphs.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Graph theory, Cayley graphs, Invariants | ||||
Official Date: | December 2017 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Georgakopoulos, Agelos | ||||
Sponsors: | Engineering and Physical Sciences Research Council ; University of Warwick. Mathematics Institute | ||||
Format of File: | |||||
Extent: | vi, 73 leaves | ||||
Language: | eng |
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