Long geodesics in subgraphs of the cube

Imre Leader, Eoin Long

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
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We show that any subgraph of the hypercube Qn of average degree d contains a geodesic of length d, where by geodesic we mean a shortest path in Qn. This result, which is best possible, strengthens a theorem of Feder and Subi. It is also related to the ‘antipodal colourings’ conjecture of Norine.
Original languageEnglish
Pages (from-to)29-33
Number of pages5
JournalDiscrete Mathematics
Early online date18 Mar 2014
Publication statusPublished - 6 Jul 2014


  • Geodesic
  • hypercube
  • antipodal colouring


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