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Gallai’s property for graphs in lattices on the torus and the Möbius strip

Abstract

We prove the existence of graphs with empty intersection of their longest paths or cycles as subgraphs of lattices on the torus and the Möbius strip.

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Acknowledgments

The second author’s work was supported by a grant of the Roumanian National Authority for Scientific Research, CNCS—UEFISCDI, project number PN-II-ID-PCE-2011-3-0533.

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Correspondence to Tudor Zamfirescu.

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Shabbir, A., Zamfirescu, T. Gallai’s property for graphs in lattices on the torus and the Möbius strip. Period Math Hung 72, 1–11 (2016). https://doi.org/10.1007/s10998-015-0105-0

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  • DOI: https://doi.org/10.1007/s10998-015-0105-0

Keywords

  • Longest paths
  • Longest cycles
  • Square lattice
  • Hexagonal lattice
  • Torus
  • Möbius strip