• Corpus ID: 2833200

The Caccetta-Haggkvist conjecture and additive number theory

  title={The Caccetta-Haggkvist conjecture and additive number theory},
  author={Melvyn B. Nathanson},
  journal={arXiv: Combinatorics},
  • M. Nathanson
  • Published 20 March 2006
  • Mathematics
  • arXiv: Combinatorics
The Caccetta-Haggkvist conjecture states that if G is a finite directed graph with at least n/k edges going out of each vertex, then G contains a directed cycle of length at most k. Hamidoune used methods and results from additive number theory to prove the conjecture for Cayley graphs and for vertex-transitive graphs. This expository paper contains a survey of results on the Caccetta-Haggkvist conjecture, and complete proofs of the conjecture in the case of Cayley and vertex-transitive graphs. 
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