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A Summary of Problems and Results related to the Caccetta-Haggkvist Conjecture

Blair Dowling Sullivan
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Abstract

This paper is an attempt to survey the current state of our knowledge on the Caccetta-Haggkvist conjecture and related questions. In January 2006 there was a workshop hosted by the American Institute of Mathematics in Palo Alto, on the Caccetta-Haggkvist conjecture, and this paper partly originated there, as a summary of the open problems and partial results presented at the workshop. This summary includes results and open problems related to Caccetta-Haggkvist, Seymour's Second Neighborhood Conjecture, the k/2 Conjecture (for nonedges), and connections with algebraic number theory through Cayley graphs, along with a number of other related topics.

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Blair Dowling Sullivan. 2006-05-24. A Summary of Problems and Results related to the Caccetta-Haggkvist Conjecture. https://arxiv.org/abs/math/0605646

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