Periodica Mathematica Hungarica

, Volume 72, Issue 1, pp 1–11 | Cite as

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

  • Ayesha Shabbir
  • Tudor Zamfirescu


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.


Longest paths Longest cycles Square lattice Hexagonal lattice Torus Möbius strip 



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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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.Abdus Salam School of Mathematical SciencesGC UniversityLahorePakistan
  2. 2.Faculty of MathematicsUniversity of DortmundDortmundGermany
  3. 3.“Simion Stoïlow” Institute of Mathematics Roumanian AcademyBucharestRoumania

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