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Grantor: Czech Science Foundation

**Objectives**:

Theories of dense and sparse graph limits are one of the most important recent tools of discrete mathematics. Their emergence and development have led to many breakthroughs on old problems in extremal graph theory and random graph theory, and especially have linked discrete mathematics to areas such as probability theory, functional analysis or group theory in a profound way. Recognitions related to the development of the field include the 2012 Fulkerson Prize, the 2013 Coxeter-James Prize, and the 2013 David P. Robbins Prize.

The project will study the theories of dense a sparse graph limits as well as the related theory of inhomogeneous random graphs. Specific problems in the area of inhomogeneous random graphs include questions on key graph parameters such as the chromatic number or the independence number. In the theory of sparse graph limits our main goal is to extend our understanding of local-global convergence. A further goal is to create a comprehensive theory of limits of subgraphs of hypercubes.

Main investigator:

IM team members:

Doležal Martin |
Pelekis Christos |