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Infinite paths in planar graphs I: Graphs with radial nets
Author(s) -
Yu Xingxing
Publication year - 2004
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.20028
Subject(s) - combinatorics , mathematics , planar graph , conjecture , graph , discrete mathematics , path (computing) , net (polyhedron) , computer science , geometry , programming language
Let G be an infinite 4‐connected planar graph such that the deletion of any finite set of vertices from G results in exactly one infinite component. Dean et al . proved that either G admits a radial net or a special subgraph of G admits a ladder net, and they used these nets to show that G contains a spanning 1‐way infinite path. In this paper, we show that if G admits a radial net, then G also contains a spanning 2‐way infinite path. This is a step towards a conjecture of Nash‐Williams. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 147–162, 2004
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