The Caccetta-Haggkvist conjecture and additive number theory

Details The Caccetta-Haggkvist conjecture and additive number theory The Caccetta-Haggkvist conjecture and additive number theory

2006-03-20

arxiv.org/abs/math/0603469v1

Mathematics

Combinatorics

14 pages; text of two lectures in the New York Number Theory Seminar

Scientific paper

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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