The Caccetta-Haggkvist conjecture and additive number theory
Combinatorics
2016-12-30 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0603469,
title = {The Caccetta-Haggkvist conjecture and additive number theory},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:math/0603469},
year = {2016}
}
Comments
14 pages; text of two lectures in the New York Number Theory Seminar