Parabolic and Hyperbolic Packings

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Abstract

In this chapter we discuss countably infinite connected simple graphs that are locally finite, that is, the vertex degrees are finite. In a similar fashion to the previous chapter, an infinite planar graph is a connected infinite graph such that there exists a drawing of it in the plane. We recall that a drawing is a correspondence sending vertices to points of ℝ2 and edges to continuous curves between the corresponding vertices such that no two edges cross. An infinite planar map is an infinite planar graph equipped with a set of cyclic permutations {σv: v ∈ V } of the neighbors of each vertex v, such that there exists a drawing of the graph which respects these permutations, that is, the clockwise order of edges emanating from a vertex v coincides with σv.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages47-60
Number of pages14
DOIs
StatePublished - 2020

Publication series

NameLecture Notes in Mathematics
Volume2243
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

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