Long paths in hypercubes with a quadratic number of faults

  • Authors:
  • Tomáš Dvořák;Václav Koubek

  • Affiliations:
  • Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00 Prague, Czech Republic;Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00 Prague, Czech Republic

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

A path between distinct vertices u and v of the n-dimensional hypercube Q"n avoiding a given set of f faulty vertices is called long if its length is at least 2^n-2f-2. We present a function @f(n)=@Q(n^2) such that if f=