## PIMS-UVic Discrete Math Seminar: Leticia Mattos

• Date: 12/03/2020
• Time: 10:15
Lecturer(s):
Leticia Mattos, IMPA
Location:

Online

Topic:

Asymmetric Ramsey properties of random graphs for cliques and cycles

Description:

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.

Other Information:

This meeting is available in person in ECS 125, or on Zoom. Gary MacGillvray can be contacted for Zoom information gmacgill@uvic.ca.