On the Maximum Degree of Path-Pairable Planar Graphs

  • António Girão
  • Gábor Mészáros
  • Kamil Popielarz
  • Richard Snyder


A graph is path-pairable if for any pairing of its vertices there exist edge-disjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in path-pairable planar graphs. We show that any $n$-vertex path-pairable planar graph must contain a vertex of degree linear in $n$. Our result generalizes to graphs embeddable on a surface of finite genus.

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