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The Caccetta-Haggkvist conjecture and additive number theory | | Melvyn B. Nathanson
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20 Mar 2006 | | Subject: | Combinatorics; 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. | | Source: | arXiv, math/0603469 | | Services: | Forum | Review | PDF | Favorites | |
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