The Caccetta-Haggkvist conjecture

January 30 to February 3, 2006

at the

American Institute of Mathematics, Palo Alto, California

organized by

Maria Chudnovsky, Paul Seymour, and Robin Thomas

This workshop, sponsored by AIM and the NSF, will focus on the Caccetta-Haggkvist conjecture, which in its simplest form asserts the following:

If G is an n-vertex directed graph with minimum outdegree at least n/k, then G has a directed cycle of length at most k.

This has a number of variants and strengthenings, and in particular it has numerous connections with additive number theory. The workshop aims to clarify and develop these variants, and to bring together people working on different aspects of the conjecture in the hope of finding a solution.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

The deadline to apply for support to participate in this workshop has passed.

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