✦ LIBER ✦

Rectangular and visibility representations of infinite planar graphs

✍ Scribed by Carsten Thomassen

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 75 KB
Volume: 52
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20160

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

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

📜 SIMILAR VOLUMES

Interval representations of planar graph

Interval representations of planar graphs

✍ Carsten Thomassen 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 867 KB

Rectangular duals of planar graphs

✍ Krzysztof Koźmiński; Edwin Kinnen 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 645 KB

Spanning paths in infinite planar graphs

✍ Dean, Nathaniel; Thomas, Robin; Yu, Xingxing 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 796 KB

Let G be a 4connected infinite planar graph such that the deletion of any finite set of vertices of G results in at most one infinite component. We prove a conjecture of Nash-Williams that G has a 1 -way infinite spanning path. 0 1996 John Wiley & Sons, Inc. [7] has shown that every 4-connected fini

Planarity testing of doubly periodic inf

Planarity testing of doubly periodic infinite graphs

✍ Kazuo Iwano; Kenneth Steiglitz 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 773 KB

Infinite paths in planar graphs V, 3-ind

Infinite paths in planar graphs V, 3-indivisible graphs

✍ Xingxing Yu 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 583 KB

## Abstract We prove Nash‐Williams' conjecture that every 4‐connected, 3‐indivisible, infinite, planar graph contains a spanning 2‐way infinite path. A graph is said to be 3‐indivisible if the deletion of any finite set of vertices results in at most two infinite components. © 2007 Wiley Periodical

Infinite paths in planar graphs III, 1-w

Infinite paths in planar graphs III, 1-way infinite paths

✍ Xingxing Yu 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 336 KB

An infinite graph is 2-indivisible if the deletion of any finite set of vertices from the graph results in exactly one infinite component. Let G be a 4-connected, 2-indivisible, infinite, plane graph. It is known that G contains a spanning 1-way infinite path. In this paper, we prove a stronger resu