Infinite paths in planar graphs V, 3-indivisible graphs

  • Authors:

  • Xingxing Yu

  • Affiliations:

  • School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 and Center for Combinatorics, Nankai University, Tianjin 300071, China

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2008

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Abstract

We prove Nash-Williams' conjecture that every 4-connected, 3-indivisible, infinite, planar graph contains a spanning 2-way infinite path. A graph is said to be 3-indivisible if the deletion of any finite set of vertices results in at most two infinite components. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 275–312, 2008