[{"ddc":["510"],"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.\r\nA. 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.","volume":62,"abstract":[{"lang":"eng","text":"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. "}],"day":"01","doi":"10.1002/rsa.21106","external_id":{"isi":["000828530400001"]},"isi":1,"year":"2023","citation":{"ama":"Liebenau A, Mattos L, Mendonca dos Santos W, Skokan J. Asymmetric Ramsey properties of random graphs involving cliques and cycles. <i>Random Structures and Algorithms</i>. 2023;62(4):1035-1055. doi:<a href=\"https://doi.org/10.1002/rsa.21106\">10.1002/rsa.21106</a>","apa":"Liebenau, A., Mattos, L., Mendonca dos Santos, W., &#38; Skokan, J. (2023). Asymmetric Ramsey properties of random graphs involving cliques and cycles. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.21106\">https://doi.org/10.1002/rsa.21106</a>","chicago":"Liebenau, Anita, Letícia Mattos, Walner Mendonca dos Santos, and Jozef Skokan. “Asymmetric Ramsey Properties of Random Graphs Involving Cliques and Cycles.” <i>Random Structures and Algorithms</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/rsa.21106\">https://doi.org/10.1002/rsa.21106</a>.","ieee":"A. Liebenau, L. Mattos, W. Mendonca dos Santos, and J. Skokan, “Asymmetric Ramsey properties of random graphs involving cliques and cycles,” <i>Random Structures and Algorithms</i>, vol. 62, no. 4. Wiley, pp. 1035–1055, 2023.","mla":"Liebenau, Anita, et al. “Asymmetric Ramsey Properties of Random Graphs Involving Cliques and Cycles.” <i>Random Structures and Algorithms</i>, vol. 62, no. 4, Wiley, 2023, pp. 1035–55, doi:<a href=\"https://doi.org/10.1002/rsa.21106\">10.1002/rsa.21106</a>.","short":"A. Liebenau, L. Mattos, W. Mendonca dos Santos, J. Skokan, Random Structures and Algorithms 62 (2023) 1035–1055.","ista":"Liebenau A, Mattos L, Mendonca dos Santos W, Skokan J. 2023. Asymmetric Ramsey properties of random graphs involving cliques and cycles. Random Structures and Algorithms. 62(4), 1035–1055."},"date_updated":"2023-10-04T09:38:45Z","article_type":"original","publisher":"Wiley","file_date_updated":"2023-10-04T09:37:26Z","quality_controlled":"1","page":"1035-1055","intvolume":"        62","title":"Asymmetric Ramsey properties of random graphs involving cliques and cycles","date_created":"2022-07-31T22:01:49Z","article_processing_charge":"Yes (in subscription journal)","department":[{"_id":"MaKw"}],"publication_status":"published","issue":"4","author":[{"last_name":"Liebenau","first_name":"Anita","full_name":"Liebenau, Anita"},{"first_name":"Letícia","last_name":"Mattos","full_name":"Mattos, Letícia"},{"first_name":"Walner","last_name":"Mendonca Dos Santos","full_name":"Mendonca Dos Santos, Walner","id":"12c6bd4d-2cd0-11ec-a0da-e28f42f65ebd"},{"full_name":"Skokan, Jozef","first_name":"Jozef","last_name":"Skokan"}],"scopus_import":"1","license":"https://creativecommons.org/licenses/by-nc/4.0/","_id":"11706","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"file_size":1362334,"checksum":"3a5969d0c512aef01c30f3dc81c6d59b","date_created":"2023-10-04T09:37:26Z","content_type":"application/pdf","file_name":"2023_RandomStructureAlgorithms_Liebenau.pdf","date_updated":"2023-10-04T09:37:26Z","access_level":"open_access","success":1,"relation":"main_file","creator":"dernst","file_id":"14389"}],"oa":1,"publication_identifier":{"eissn":["1098-2418"],"issn":["1042-9832"]},"type":"journal_article","date_published":"2023-07-01T00:00:00Z","tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"language":[{"iso":"eng"}],"month":"07","oa_version":"Published Version","has_accepted_license":"1","publication":"Random Structures and Algorithms"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.07746"}],"status":"public","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","type":"journal_article","date_published":"2018-12-01T00:00:00Z","publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"oa":1,"language":[{"iso":"eng"}],"publication":"Random Structures and Algorithms","oa_version":"Preprint","month":"12","volume":53,"extern":"1","year":"2018","citation":{"ista":"Ferber A, Kwan MA, Sudakov B. 2018. Counting Hamilton cycles in sparse random directed graphs. Random Structures and Algorithms. 53(4), 592–603.","short":"A. Ferber, M.A. Kwan, B. Sudakov, Random Structures and Algorithms 53 (2018) 592–603.","mla":"Ferber, Asaf, et al. “Counting Hamilton Cycles in Sparse Random Directed Graphs.” <i>Random Structures and Algorithms</i>, vol. 53, no. 4, Wiley, 2018, pp. 592–603, doi:<a href=\"https://doi.org/10.1002/rsa.20815\">10.1002/rsa.20815</a>.","ieee":"A. Ferber, M. A. Kwan, and B. Sudakov, “Counting Hamilton cycles in sparse random directed graphs,” <i>Random Structures and Algorithms</i>, vol. 53, no. 4. Wiley, pp. 592–603, 2018.","chicago":"Ferber, Asaf, Matthew Alan Kwan, and Benny Sudakov. “Counting Hamilton Cycles in Sparse Random Directed Graphs.” <i>Random Structures and Algorithms</i>. Wiley, 2018. <a href=\"https://doi.org/10.1002/rsa.20815\">https://doi.org/10.1002/rsa.20815</a>.","ama":"Ferber A, Kwan MA, Sudakov B. Counting Hamilton cycles in sparse random directed graphs. <i>Random Structures and Algorithms</i>. 2018;53(4):592-603. doi:<a href=\"https://doi.org/10.1002/rsa.20815\">10.1002/rsa.20815</a>","apa":"Ferber, A., Kwan, M. A., &#38; Sudakov, B. (2018). Counting Hamilton cycles in sparse random directed graphs. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.20815\">https://doi.org/10.1002/rsa.20815</a>"},"date_updated":"2023-02-23T14:01:03Z","external_id":{"arxiv":["1708.07746"]},"day":"01","arxiv":1,"doi":"10.1002/rsa.20815","abstract":[{"text":"Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if p≥(logn+ω(1))/n then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically n!(p(1+o(1)))n. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically n!(logn/n(1+o(1)))n directed Hamilton cycles.","lang":"eng"}],"quality_controlled":"1","page":"592-603","publisher":"Wiley","article_type":"original","scopus_import":"1","_id":"9565","issue":"4","author":[{"full_name":"Ferber, Asaf","last_name":"Ferber","first_name":"Asaf"},{"first_name":"Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"first_name":"Benny","last_name":"Sudakov","full_name":"Sudakov, Benny"}],"article_processing_charge":"No","date_created":"2021-06-18T12:06:28Z","publication_status":"published","intvolume":"        53","title":"Counting Hamilton cycles in sparse random directed graphs"},{"article_type":"original","publisher":"Wiley","page":"692-716","quality_controlled":"1","title":"The random k‐matching‐free process","intvolume":"        53","publication_status":"published","date_created":"2021-06-18T12:37:40Z","article_processing_charge":"No","author":[{"full_name":"Krivelevich, Michael","first_name":"Michael","last_name":"Krivelevich"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","last_name":"Kwan"},{"full_name":"Loh, Po‐Shen","last_name":"Loh","first_name":"Po‐Shen"},{"last_name":"Sudakov","first_name":"Benny","full_name":"Sudakov, Benny"}],"issue":"4","_id":"9567","scopus_import":"1","extern":"1","volume":53,"abstract":[{"lang":"eng","text":"Let P be a graph property which is preserved by removal of edges, and consider the random graph process that starts with the empty n-vertex graph and then adds edges one-by-one, each chosen uniformly at random subject to the constraint that P is not violated. These types of random processes have been the subject of extensive research over the last 20 years, having striking applications in extremal combinatorics, and leading to the discovery of important probabilistic tools. In this paper we consider the k-matching-free process, where P is the property of not containing a matching of size k. We are able to analyse the behaviour of this process for a wide range of values of k; in particular we prove that if k=o(n) or if n−2k=o(n−−√/logn) then this process is likely to terminate in a k-matching-free graph with the maximum possible number of edges, as characterised by Erdős and Gallai. We also show that these bounds on k are essentially best possible, and we make a first step towards understanding the behaviour of the process in the intermediate regime."}],"arxiv":1,"doi":"10.1002/rsa.20814","day":"01","external_id":{"arxiv":["1708.01054"]},"date_updated":"2023-02-23T14:01:07Z","year":"2018","citation":{"apa":"Krivelevich, M., Kwan, M. A., Loh, P., &#38; Sudakov, B. (2018). The random k‐matching‐free process. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.20814\">https://doi.org/10.1002/rsa.20814</a>","ama":"Krivelevich M, Kwan MA, Loh P, Sudakov B. The random k‐matching‐free process. <i>Random Structures and Algorithms</i>. 2018;53(4):692-716. doi:<a href=\"https://doi.org/10.1002/rsa.20814\">10.1002/rsa.20814</a>","ieee":"M. Krivelevich, M. A. Kwan, P. Loh, and B. Sudakov, “The random k‐matching‐free process,” <i>Random Structures and Algorithms</i>, vol. 53, no. 4. Wiley, pp. 692–716, 2018.","chicago":"Krivelevich, Michael, Matthew Alan Kwan, Po‐Shen Loh, and Benny Sudakov. “The Random K‐matching‐free Process.” <i>Random Structures and Algorithms</i>. Wiley, 2018. <a href=\"https://doi.org/10.1002/rsa.20814\">https://doi.org/10.1002/rsa.20814</a>.","mla":"Krivelevich, Michael, et al. “The Random K‐matching‐free Process.” <i>Random Structures and Algorithms</i>, vol. 53, no. 4, Wiley, 2018, pp. 692–716, doi:<a href=\"https://doi.org/10.1002/rsa.20814\">10.1002/rsa.20814</a>.","short":"M. Krivelevich, M.A. Kwan, P. Loh, B. Sudakov, Random Structures and Algorithms 53 (2018) 692–716.","ista":"Krivelevich M, Kwan MA, Loh P, Sudakov B. 2018. The random k‐matching‐free process. Random Structures and Algorithms. 53(4), 692–716."},"language":[{"iso":"eng"}],"month":"12","oa_version":"Preprint","publication":"Random Structures and Algorithms","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1708.01054","open_access":"1"}],"oa":1,"publication_identifier":{"eissn":["1098-2418"],"issn":["1042-9832"]},"date_published":"2018-12-01T00:00:00Z","type":"journal_article"},{"abstract":[{"lang":"eng","text":"An intercalate in a Latin square is a 2×2 Latin subsquare. Let N be the number of intercalates in a uniformly random n×n Latin square. We prove that asymptotically almost surely N≥(1−o(1))n2/4, and that EN≤(1+o(1))n2/2 (therefore asymptotically almost surely N≤fn2 for any f→∞). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares."}],"doi":"10.1002/rsa.20742","arxiv":1,"day":"01","external_id":{"arxiv":["1607.04981"]},"date_updated":"2023-02-23T14:01:09Z","citation":{"ama":"Kwan MA, Sudakov B. Intercalates and discrepancy in random Latin squares. <i>Random Structures and Algorithms</i>. 2018;52(2):181-196. doi:<a href=\"https://doi.org/10.1002/rsa.20742\">10.1002/rsa.20742</a>","apa":"Kwan, M. A., &#38; Sudakov, B. (2018). Intercalates and discrepancy in random Latin squares. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.20742\">https://doi.org/10.1002/rsa.20742</a>","chicago":"Kwan, Matthew Alan, and Benny Sudakov. “Intercalates and Discrepancy in Random Latin Squares.” <i>Random Structures and Algorithms</i>. Wiley, 2018. <a href=\"https://doi.org/10.1002/rsa.20742\">https://doi.org/10.1002/rsa.20742</a>.","ieee":"M. A. Kwan and B. Sudakov, “Intercalates and discrepancy in random Latin squares,” <i>Random Structures and Algorithms</i>, vol. 52, no. 2. Wiley, pp. 181–196, 2018.","mla":"Kwan, Matthew Alan, and Benny Sudakov. “Intercalates and Discrepancy in Random Latin Squares.” <i>Random Structures and Algorithms</i>, vol. 52, no. 2, Wiley, 2018, pp. 181–96, doi:<a href=\"https://doi.org/10.1002/rsa.20742\">10.1002/rsa.20742</a>.","short":"M.A. Kwan, B. Sudakov, Random Structures and Algorithms 52 (2018) 181–196.","ista":"Kwan MA, Sudakov B. 2018. Intercalates and discrepancy in random Latin squares. Random Structures and Algorithms. 52(2), 181–196."},"year":"2018","extern":"1","volume":52,"title":"Intercalates and discrepancy in random Latin squares","intvolume":"        52","publication_status":"published","article_processing_charge":"No","date_created":"2021-06-18T12:47:25Z","author":[{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"},{"last_name":"Sudakov","first_name":"Benny","full_name":"Sudakov, Benny"}],"issue":"2","_id":"9568","scopus_import":"1","article_type":"original","publisher":"Wiley","page":"181-196","quality_controlled":"1","oa":1,"publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"date_published":"2018-03-01T00:00:00Z","type":"journal_article","status":"public","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","main_file_link":[{"url":"https://arxiv.org/abs/1607.04981","open_access":"1"}],"month":"03","oa_version":"Preprint","publication":"Random Structures and Algorithms","language":[{"iso":"eng"}]},{"author":[{"full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"full_name":"Thorup, Mikkel","last_name":"Thorup","first_name":"Mikkel"}],"issue":"4","_id":"11883","publication":"Random Structures and Algorithms","scopus_import":"1","month":"12","title":"Sampling to provide or to bound: With applications to fully dynamic graph algorithms","intvolume":"        11","publication_status":"published","oa_version":"None","date_created":"2022-08-17T07:21:55Z","article_processing_charge":"No","language":[{"iso":"eng"}],"page":"369-379","quality_controlled":"1","article_type":"original","publisher":"Wiley","date_published":"1997-12-07T00:00:00Z","type":"journal_article","date_updated":"2023-02-17T14:05:02Z","citation":{"chicago":"Henzinger, Monika H, and Mikkel Thorup. “Sampling to Provide or to Bound: With Applications to Fully Dynamic Graph Algorithms.” <i>Random Structures and Algorithms</i>. Wiley, 1997. <a href=\"https://doi.org/10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x\">https://doi.org/10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x</a>.","ieee":"M. H. Henzinger and M. Thorup, “Sampling to provide or to bound: With applications to fully dynamic graph algorithms,” <i>Random Structures and Algorithms</i>, vol. 11, no. 4. Wiley, pp. 369–379, 1997.","ama":"Henzinger MH, Thorup M. Sampling to provide or to bound: With applications to fully dynamic graph algorithms. <i>Random Structures and Algorithms</i>. 1997;11(4):369-379. doi:<a href=\"https://doi.org/10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x\">10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x</a>","apa":"Henzinger, M. H., &#38; Thorup, M. (1997). Sampling to provide or to bound: With applications to fully dynamic graph algorithms. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x\">https://doi.org/10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x</a>","ista":"Henzinger MH, Thorup M. 1997. Sampling to provide or to bound: With applications to fully dynamic graph algorithms. Random Structures and Algorithms. 11(4), 369–379.","short":"M.H. Henzinger, M. Thorup, Random Structures and Algorithms 11 (1997) 369–379.","mla":"Henzinger, Monika H., and Mikkel Thorup. “Sampling to Provide or to Bound: With Applications to Fully Dynamic Graph Algorithms.” <i>Random Structures and Algorithms</i>, vol. 11, no. 4, Wiley, 1997, pp. 369–79, doi:<a href=\"https://doi.org/10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x\">10.1002/(sici)1098-2418(199712)11:4&#60;369::aid-rsa5&#62;3.0.co;2-x</a>."},"year":"1997","abstract":[{"lang":"eng","text":"In dynamic graph algorithms the following provide-or-bound problem has to be solved quickly: Given a set S containing a subset R and a way of generating random elements from S testing for membership in R, either (i) provide an element of R, or (ii) give a (small) upper bound on the size of R that holds with high probability. We give an optimal algorithm for this problem. This algorithm improves the time per operation for various dynamic graph algorithms by a factor of O(log n). For example, it improves the time per update for fully dynamic connectivity from O(log3n) to O(log2n)."}],"doi":"10.1002/(sici)1098-2418(199712)11:4<369::aid-rsa5>3.0.co;2-x","publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"day":"07","extern":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":11}]