Asymmetric Ramsey properties of random graphs involving cliques and cycles
Liebenau, A., Mattos, L., Mendonça, W. & Skokan, J.
(2019).
Asymmetric Ramsey properties of random graphs involving cliques and cycles.
Acta Mathematica Universitatis Comenianae,
88(3), 917 - 922.
(2019).
Asymmetric Ramsey properties of random graphs involving cliques and cycles.
Acta Mathematica Universitatis Comenianae,
88(3), 917 - 922.
We prove that for every ℓ, r ≥ 3, there exists c > 0 such that for (image found), with high probability there is a 2-edge-colouring of the random graph Gn,p with no monochromatic copy of Kr of the first colour and no monochromatic copy of Cℓ of the second colour. This is a progress on a conjecture of Kohayakawa and Kreuter.