Asymmetric Ramsey properties of random graphs involving cliques and cycles

Liebenau A, Mattos L, Mendonca dos Santos W, Skokan J. 2022. Asymmetric Ramsey properties of random graphs involving cliques and cycles. Random Structures and Algorithms.


Journal Article | Epub ahead of print | English

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Author
Liebenau, Anita; Mattos, Letícia; Mendonca dos Santos, WalnerISTA; Skokan, Jozef
Department
Abstract
We say that (Formula presented.) if, in every edge coloring (Formula presented.), we can find either a 1-colored copy of (Formula presented.) or a 2-colored copy of (Formula presented.). The well-known states that the threshold for the property (Formula presented.) is equal to (Formula presented.), where (Formula presented.) is given by (Formula presented.) for any pair of graphs (Formula presented.) and (Formula presented.) with (Formula presented.). In this article, we show the 0-statement of the Kohayakawa–Kreuter conjecture for every pair of cycles and cliques.
Publishing Year
Date Published
2022-07-21
Journal Title
Random Structures and Algorithms
Acknowledgement
This work was started at the thematic program GRAPHS@IMPA (January–March 2018), in Rio de Janeiro. We thank IMPA and the organisers for the hospitality and for providing a pleasant research environment. We thank Rob Morris for helpful discussions, and the anonymous referees for their careful reading and many helpful suggestions. Open Access funding enabled and organized by Projekt DEAL. A. Liebenau was supported by an ARC DECRA Fellowship Grant DE170100789. L. Mattos was supported by CAPES and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689). W. Mendonça was supported by CAPES project 88882.332408/2010-01.
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Cite this

Liebenau A, Mattos L, Mendonca dos Santos W, Skokan J. Asymmetric Ramsey properties of random graphs involving cliques and cycles. Random Structures and Algorithms. 2022. doi:10.1002/rsa.21106
Liebenau, A., Mattos, L., Mendonca dos Santos, W., & Skokan, J. (2022). Asymmetric Ramsey properties of random graphs involving cliques and cycles. Random Structures and Algorithms. Wiley. https://doi.org/10.1002/rsa.21106
Liebenau, Anita, Letícia Mattos, Walner Mendonca dos Santos, and Jozef Skokan. “Asymmetric Ramsey Properties of Random Graphs Involving Cliques and Cycles.” Random Structures and Algorithms. Wiley, 2022. https://doi.org/10.1002/rsa.21106.
A. Liebenau, L. Mattos, W. Mendonca dos Santos, and J. Skokan, “Asymmetric Ramsey properties of random graphs involving cliques and cycles,” Random Structures and Algorithms. Wiley, 2022.
Liebenau A, Mattos L, Mendonca dos Santos W, Skokan J. 2022. Asymmetric Ramsey properties of random graphs involving cliques and cycles. Random Structures and Algorithms.
Liebenau, Anita, et al. “Asymmetric Ramsey Properties of Random Graphs Involving Cliques and Cycles.” Random Structures and Algorithms, Wiley, 2022, doi:10.1002/rsa.21106.
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