Abstract.
It was conjectured by Caccetta and Häggkvist in 1978 that every digraph G with n vertices and minimum outdegree at least r contains a directed cycle of length at most ⌈n/r⌉. By refining an argument of Chvátal and Szemerédi, we prove that such G contains a directed cycle of length at most n/r+73.
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Received: September 13, 1999 Final version received: June 19, 2000
Acknowledgment. I want to thank a referee for many valuable suggestions leading to the clear presentation of the paper.
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Shen, J. On the Caccetta–Häggkvist Conjecture. Graphs Comb 18, 645–654 (2002). https://doi.org/10.1007/s003730200048
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DOI: https://doi.org/10.1007/s003730200048