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

✍ Scribed by Xingxing Yu

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 336 KB
Volume: 51
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20130

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✦ Synopsis

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 result by showing that, for any vertex x and any edge e on a facial cycle of G, there is a spanning 1-way infinite path in G from x and through e. Results will be used in two forthcoming papers to establish a conjecture of Nash-Williams.

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