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Asymmetric Ramsey properties of random graphs involving cliques and cycles

Liebenau, Anita, Mattos, Letícia, Mendonça, Walner and Skokan, Jozef ORCID: 0000-0003-3996-7676 (2022) Asymmetric Ramsey properties of random graphs involving cliques and cycles. Random Structures & Algorithms. ISSN 1042-9832

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Identification Number: 10.1002/rsa.21106

Abstract

We say thatG→(F,H)if, in every edge coloringc∶E(G)→{1,2}, we can find either a 1-colored copy ofFor a 2-colored copy ofH. The well-known states thatthe threshold for the propertyG(n,p)→(F,H)is equal ton−1∕m2(F,H),wherem2(F,H)is given bym2(F,H)∶=max{e(J)v(J)−2+1∕m2(H)∶J⊆F,e(J)≥1},for any pair of graphsFandHwithm2(F)≥m2(H).In this article, we show the 0-statement of the Kohayakawa–Kreuter conjecture for every pair of cycles and cliques.

Item Type: Article
Official URL: https://onlinelibrary.wiley.com/journal/10982418
Additional Information: © 2022 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 22 Jul 2022 09:45
Last Modified: 12 Sep 2022 23:21
URI: http://eprints.lse.ac.uk/id/eprint/115628

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