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.