Large substructures in random graphs and hypergraphs

• Grant number: 21/11020-9
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 01, 2022
• End date: April 21, 2022
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Yoshiharu Kohayakawa
• Grantee: Yoshiharu Kohayakawa
• Visiting researcher: Richard Lang
• Visiting researcher institution: Heidelberg University, Germany
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics, AP.JP

Abstract

This grant will support the visit of Richard Lang, University of Heidelberg, Germany, to the Institute of Mathematics and Statistics of the University of São Paulo (IME/USP), from 1 March to 31 May 2022 (3 months). The visitor and members of the research group in combinatorics at IME/USP, including young researchers and students, will work on two classes of problems in the area of probabilistic combinatorics: (i) Dirac-type problems in the context of random hypergraphs, and (ii) problems involving monochromatic coverings of edge-coloured random graphs, inspired by problems of Ryser and Lovász. For (i), we shall consider approaches based on the regularity method, the absorption method and the method of templates, together with additional ideas developed by the visitor in joint work with Sanhueza-Matamala. For (ii), among others, approaches based on transversals of hypergraphs will be considered. The visitor will give talks on his recent work at USP and other institutions. (AU)