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Infinite paths in planar graphs III, 1‐way infinite paths
Author(s) -
Yu Xingxing
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.20130
Subject(s) - combinatorics , mathematics , planar graph , conjecture , discrete mathematics , vertex (graph theory) , graph
Abstract 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. © 2005 Wiley Periodicals, Inc. J Graph Theory