• Corpus ID: 233864385

Ramsey numbers of sparse digraphs

@inproceedings{Fox2021RamseyNO,
  title={Ramsey numbers of sparse digraphs},
  author={Jacob Fox and Xiaoyu He and Yuval Wigderson},
  year={2021}
}
Burr and Erdős in 1975 conjectured, and Chvátal, Rödl, Szemerédi and Trotter later proved, that the Ramsey number of any bounded degree graph is linear in the number of vertices. In this paper, we disprove the natural directed analogue of the Burr–Erdős conjecture, answering a question of Bucić, Letzter, and Sudakov. If H is an acyclic digraph, the oriented Ramsey number of H , denoted r1(H), is the least N such that every tournament on N vertices contains a copy of H . We show that for any… 

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