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Infinitely Many Hypohamiltonian Cubic Graphs of Girth 7

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Abstract

The trivalent Coxeter graph of order 28 is the only known hypohamiltonian cubic graph of girth 7. In this paper we will construct an infinite family of hypohamiltonian cubic graphs of girth 7 and cyclic connectivity 6. The existence of cyclically 7-edge-connected hypohamiltonian cubic graphs other than the Coxeter graph, however, remains open.

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48, Bratislava, Slovakia

    Edita Máčajová & Martin Škoviera

Authors
  1. Edita Máčajová
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  2. Martin Škoviera
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Correspondence to Edita Máčajová.

Additional information

Research partially supported by APVV-0111-07 and by VEGA grant 1/0634/09.

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Máčajová, E., Škoviera, M. Infinitely Many Hypohamiltonian Cubic Graphs of Girth 7. Graphs and Combinatorics 27, 231–241 (2011). https://doi.org/10.1007/s00373-010-0968-z

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  • DOI: https://doi.org/10.1007/s00373-010-0968-z

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