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Minimal k-Connected Non-Hamiltonian Graphs

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Abstract

In this paper, we explore minimal k-connected non-Hamiltonian graphs. Graphs are said to be minimal in the context of some containment relation; we focus on subgraphs, induced subgraphs, minors, and induced minors. When \(k=2\), we discuss all minimal 2-connected non-Hamiltonian graphs for each of these four relations. When \(k=3\), we conjecture a set of minimal non-Hamiltonian graphs for the minor relation and we prove one case of this conjecture. In particular, we prove all 3-connected planar triangulations which do not contain the Herschel graph as a minor are Hamiltonian.

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Authors and Affiliations

  1. Mathematics Department, Louisiana State University, Baton Rouge, LA, 70803, USA

    Guoli Ding

  2. Computer Science and Mathematics Department, Arcadia University, Glenside, PA, 19038, USA

    Emily Marshall

Authors
  1. Guoli Ding
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  2. Emily Marshall
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Corresponding author

Correspondence to Emily Marshall.

Additional information

The first author was supported in part by NSF Grant DMS-1500699.

The work for this paper was largely done while the second author was at Louisiana State University.

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Ding, G., Marshall, E. Minimal k-Connected Non-Hamiltonian Graphs. Graphs and Combinatorics 34, 289–312 (2018). https://doi.org/10.1007/s00373-018-1874-z

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  • DOI: https://doi.org/10.1007/s00373-018-1874-z

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