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Turan-type problems for graphs and hypergraphs

Turan-type problems for graphs and hypergraphs

Objective

In this project, we propose to study several Turan-type extremal problems for graphs and hypergraphs as well as related extremal problems on rainbow structures. In Turan-type extremal problems, roughly speaking, we want to determine how dense a configuration (graph, hypergraph, set system, etc.) can be when certain sub-configurations are forbidden. One of the earliest results in the area is Mantel's Theorem from 1908, which says that the largest triangle-free graph on given number of vertices is the balanced complete bipartite graph. This was generalized by Turan in 1941 to complete graphs on any number of vertices. The Turan-number of a graph G is the largest number of edges that a graph on given number of vertices can have without containing G.

The experienced researcher in recent years has made several contributions to these problems. On Turan-type problems for bipartite graphs, in joint work with Jiang and Ma, the she made a first non-trivial progress in a while to a conjecture of Erdos and Simonovits regarding the so-called Turan exponents of single bipartite graphs. On hypergraph Turan-type problems, in joint work with Sergey Norin, she has developed a highly effective variant of the classical stability method that allowed them to solve several open conjectures in the field. The TC-supervisor, Dhruv Mubayi, is a world leading expert on Turan-type extremal problems. Working on problems posed in this proposal will allow the experienced researcher to further develop these promising tools with a leading expert.

The second set of problems concern rainbow structures in edge-coloured graphs and hypergraphs. The experienced researcher, in joint works with Peter Keevash, and also with others had made several contributions to this area in the last two years. Here there is also a common theme of a series of work done by the MC-supervisor Julia Boettcher, who is a leading expert on the study of spanning structures in graphs and hypergraphs.
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Coordinator

LONDON SCHOOL OF ECONOMICS AND POLITICAL SCIENCE

Address

Houghton Street 1
Wc2a 2ae London

United Kingdom

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 271 732,80

Partners (1)

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The University of Illinois at Chicago

Project information

Grant agreement ID: 846304

Status

Grant agreement signed

  • Start date

    1 September 2019

  • End date

    31 August 2022

Funded under:

H2020-EU.1.3.2.

  • Overall budget:

    € 271 732,80

  • EU contribution

    € 271 732,80

Coordinated by:

LONDON SCHOOL OF ECONOMICS AND POLITICAL SCIENCE

United Kingdom