Geodesic
Asymmetric Ramsey properties of random graphs involving cliques and cycles
Anita Liebenau1 ; Letícia Mattos2 ; Walner Mendonça2 ; Jozef Skokan3 ; Anita Liebenau ; Letícia Mattos ; Walner Mendonça ; Jozef Skokan
1School of Mathematics and Statistics, University of New South Wales, Sydney, Australia
2Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
3Department of Mathematics, London School of Economics, London, UK
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 917-922 
Anita Liebenau; Letícia Mattos; Walner Mendonça; Jozef Skokan; Anita Liebenau; Letícia Mattos; Walner Mendonça; Jozef Skokan. Asymmetric Ramsey properties of random graphs involving cliques and cycles. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 917-922. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a86/
@article{AMUC_2019_88_3_a86,
     author = {Anita Liebenau and Let{\'\i}cia Mattos and Walner Mendon\c{c}a and Jozef Skokan and Anita Liebenau and Let{\'\i}cia Mattos and Walner Mendon\c{c}a and Jozef Skokan},
     title = { Asymmetric {Ramsey} properties of random graphs involving cliques and cycles},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {917--922},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a86/}
}
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Voir la notice de l'article provenant de la source Comenius University

We prove that for every $\ell,r \geq 3$, there exists $c>0$ such that for $p \leq cn^{-1/m_2(K_r,C_{\ell})}$, with high probability there is a 2-edge-colouring of the random graph $\gnp$ with no monochromatic copy of $K_r$ of the first colour and no monochromatic copy of $C_\ell$ of the second colour. This is a progress on a conjecture of Kohayakawa and Kreuter.