On the number of contractible triples in 3-connected graphs

  • Authors:

  • Matthias Kriesell

  • Affiliations:

  • Mathematisches Seminar der Universität Hamburg, Bundesstraße 55, D-20146 Hamburg, Germany

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2008

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Abstract

McCuaig and Ota proved that every 3-connected graph G on at least 9 vertices admits a contractible triple, i.e. a connected subgraph H on three vertices such that G-V(H) is 2-connected. Here we show that every 3-connected graph G on at least 9 vertices has more than |V(G)|/10 many contractible triples. If, moreover, G is cubic, then there are at least |V(G)|/3 many contractible triples, which is best possible.