A note on the girth of digraphs

Abstract

Behzad, Chartrand and Wall conjectured that the girth of a diregular graph of ordern and outdegreer is not greater than [n /r]. This conjecture has been proved forr=2 by Behzad and forr=3 by Bermond. We prove that a digraph of ordern and halfdegree ≧4 has girth not exceeding [n / 4]. We also obtain short proofs of the above results. Our method is an application of the theory of connectivity of digraphs.

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Hamidoune, Y.O. A note on the girth of digraphs. Combinatorica 2, 143–147 (1982). https://doi.org/10.1007/BF02579312

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AMS subject classification (1980)

  • 05 C 20
  • 05 C 38
  • 05 C 35
  • 05 C 40