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Hypohamiltonian graphs and digraphs

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Theory and Applications of Graphs

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 642))

Abstract

Methods for constructing hypohamiltonian graphs and oriented graphs are described. It is shown that every planar hypohamiltonian graph contains a vertex of degree 3 and that for each n ≥ 6 there exists a planar, hypohamiltonian digraph with n vertices. Finally it is proved that every graph with n vertices contains a set A of at most 1/3n vertices such that every longest cycle of the graph intersects A.

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Author information

Authors and Affiliations

  1. University of Waterloo, Waterloo, Ontario, Canada

    Carsten Thomassen

Authors
  1. Carsten Thomassen
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA

    Yousef Alavi  & Don R. Lick  & 

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© 1978 Springer-Verlag Berlin Heidelberg

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Thomassen, C. (1978). Hypohamiltonian graphs and digraphs. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070410

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  • DOI: https://doi.org/10.1007/BFb0070410

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08666-6

  • Online ISBN: 978-3-540-35912-8

  • eBook Packages: Springer Book Archive

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