TY - CHAP

T1 - Parabolic and Hyperbolic Packings

AU - Nachmias, Asaf

N1 - Publisher Copyright:
© 2020, The Author(s).

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85073170981&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-27968-4_4

DO - 10.1007/978-3-030-27968-4_4

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AN - SCOPUS:85073170981

T3 - Lecture Notes in Mathematics

SP - 47

EP - 60

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -