Rectangular and visibility representations of infinite planar graphs | Zendy

Thomassen Carsten | Zendy

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Rectangular and visibility representations of infinite planar graphs

Author(s) -

Thomassen Carsten

Publication year - 2006

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.20160

Subject(s) - planar graph , mathematics , combinatorics , outerplanar graph , line graph , discrete mathematics , planar straight line graph , visibility graph , graph , polyhedral graph , 1 planar graph , voltage graph , geometry , regular polygon

We provide a new method for extending results on finite planar graphs to the infinite case. Thus a result of Ungar on finite graphs has the following extension: Every infinite, planar, cubic, cyclically 4‐edge‐connected graph has a representation in the plane such that every edge is a horizontal or vertical straight line segment, and such that no two edges cross. A result of Tamassia and Tollis extends as follows: Every countably infinite planar graph is a subgraph of a visibility graph. Furthermore, every locally finite, 2‐connected, planar graph is a visibility graph. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 257–265, 2006

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