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Hamiltonicity of Amalgams

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Abstract.

 An amalgam is obtained from two Halin graphs having skirting cycles of the same length. We are interested in hamiltonicity of amalgams constructed from two identical Halin graphs without any shift along the skirting cycle. We establish hamiltonicity of amalagams constructed from cubic Halin graphs. We give a sufficient condition for hamiltonicity of non-cubic amalgams and characterize infinite classes of non-Hamiltonian amalgams. We also characterize hamiltonicity of amalgams constructed by shifting the component Halin graphs by one and of general amalgams of higher degree.

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Authors and Affiliations

  1.  Department of Computer and Information Science, University of Oregon, Eugene, OR 97403, USA, , , , , , US

    Arthur M. Farley

  2.  Department of Computer and Information Science, University of Oregon, Eugene, OR 97403, USA. e-mail: andrzej@cs.uoregon.edu, , , , , , US

    Andrzej Proskurowski

  3.  Faculty of Mathematics and Informatics, Nicholas Copernicus University, ul. Chopina 12/18, 87100 Toruń, Poland, , , , , , PL

    Mirosława Skowrońska

  4.  Institute of Computer Science, University of Wrocław, ul. Przesmyckiego 20, 51151 Wrocław, Poland, , , , , , PL

    Maciej M. Sysło

Authors
  1. Arthur M. Farley
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  2. Andrzej Proskurowski
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  3. Mirosława Skowrońska
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  4. Maciej M. Sysło
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Received: June 23, 1997

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Farley, A., Proskurowski, A., Skowrońska, M. et al. Hamiltonicity of Amalgams. Graphs Comb 15, 393–404 (1999). https://doi.org/10.1007/s003730050048

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  • DOI: https://doi.org/10.1007/s003730050048

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