Infinite paths in planar graphs I: Graphs with radial nets

  • Authors:

  • Xingxing Yu

  • Affiliations:

  • School of Mathematics, Georgia Institute of Technology, Atlanta, GA and Center for Combinatorics, Nankai University, Tianjin 300071, China

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2004

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Abstract

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