PIMS-UVic Discrete Math Seminar: Leticia Mattos

Abstract

We say that \(G\to (F, H)\) if, in every edge colouring \(c : E(G) \to \{1, 2\}\), we can find either a 1-coloured copy of \(F\) or a 2-coloured copy of \(H\). The well-known Kohayakawa-Kreuter conjecture states that the threshold for the property \(G(n, p)\to (F, H)\) is equal to \(n^{{1/m_2}(F, H)}\) where \(m_2(F, H)\) is given by $$ m_2(F, H) := \max{\left\{ \frac{e(J)}{v(J) - 2 + 1/m_2(H)} : J\subseteq F, e(J) \geq 1 \right\}}. $$ In this talk, we show that the 0-statement of the Kohayakawa-Kreuter conjecture holds for every pair of cycles and cliques.

Joint work with Anitia Linebau, Walter Mendoca and Jozef Skokan.