Long paths in sparse random graphs

Abstract

We consider random graphs withn labelled vertices in which edges are chosen independently and with probabilityc/n. We prove that almost every random graph of this kind contains a path of length ≧(1 −α(c))n where α(c) is an exponentially decreasing function ofc.

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Dedicated to Tibor Gallai on his seventieth birthday

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Bollobás, B. Long paths in sparse random graphs. Combinatorica 2, 223–228 (1982). https://doi.org/10.1007/BF02579230

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AMS subject classification (1980)

  • 05 C 38
  • 60 C 05