Graphs and Combinatorics

, Volume 29, Issue 4, pp 729–733

An Infinite Family of Planar Hypohamiltonian Oriented Graphs

  • Susan A. van Aardt
  • Alewyn P. Burger
  • Marietjie Frick
Original Paper

Abstract

Carsten Thomassen asked in 1976 whether there exists a planar hypohamiltonian oriented graph. We answer his question by presenting an infinite family of planar hypohamiltonian oriented graphs, the smallest of which has order 9. A computer search showed that 9 is the smallest possible order of a hypohamiltonian oriented graph.

Keywords

Hypohamiltonian Bihomogeneously traceable Oriented graph Planar graph 

Mathematics Subject Classification

05C20 05C38 

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Copyright information

© Springer 2012

Authors and Affiliations

  • Susan A. van Aardt
    • 1
  • Alewyn P. Burger
    • 2
  • Marietjie Frick
    • 1
  1. 1.Department of Mathematical SciencesUniversity of South Africa (UNISA)PretoriaSouth Africa
  2. 2.Department of LogisticsUniversity of StellenboschStellenboschSouth Africa

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