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Infinite paths in planar graphs II, structures and ladder nets

✍ Scribed by Xingxing Yu

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 217 KB
Volume: 48
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20054

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✦ Synopsis

Abstract

A graph is k‐indivisible, where k is a positive integer, if the deletion of any finite set of vertices results in at most k – 1 infinite components. In 1971, Nash‐Williams conjectured that a 4‐connected infinite planar graph contains a spanning 2‐way infinite path if and only if it is 3‐indivisible. In this paper, we prove a structural result for 2‐indivisible infinite planar graphs. This structural result is then used to prove Nash‐Williams conjecture for all 4‐connected 2‐indivisible infinite planar graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 247–266, 2005

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