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Hamiltonian cycles in some family of cubic 3-connected plane graphs

Volume 151 / 2018

Jan Florek Colloquium Mathematicum 151 (2018), 229-274 MSC: 05C45, 05C05. DOI: 10.4064/cm7123-9-2017 Published online: 20 December 2017


Barnette conjectured that all cubic 3-connected plane graphs with maximum face size at most 6 are hamiltonian. We provide a method of construction of a hamiltonian cycle in an arbitrary 3-connected cubic plane graph possessing a face $f$ (of arbitrary size) such that every face incident with $f$ is bounded by at most five edges and any other face is bounded by at most six edges. The method works for a larger family of graphs where many faces may have arbitrary sizes.


  • Jan FlorekFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland

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