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LArge STructures IN random Graphs

The study of random graphs lies in the interface between combinatorics, graph theory, and probability, and has a tremendous amount of applications in various fields such as networks, algorithms, physics, and life sciences. The aim... ver más

30/06/2023

UOXF

225K€

Presupuesto del proyecto: 225K€

Líder del proyecto

THE CHANCELLOR MASTERS AND SCHOLARS OF THE UN... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2023-06-30

MSCA-IF-2020: Individual Fellowships

I+D

Cerrada hace 4 años

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1 Participantes

UOXF

224.93K€ | Lider

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Duración del proyecto: 26 meses Fecha Inicio: 2021-04-07
Fecha Fin: 2023-06-30

Líder del proyecto

THE CHANCELLOR MASTERS AND SCHOLARS OF THE UN... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 225K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The study of random graphs lies in the interface between combinatorics, graph theory, and probability, and has a tremendous amount of applications in various fields such as networks, algorithms, physics, and life sciences. The aim of this project is to study large structures in random graphs, count their appearances and measure their strength. In the first set of problems we aim to count the number of subgraphs from specific families in random graphs, where the families contain both large and small members. We consider families such as cycles, matchings, trees, and independent sets. In combinatorics, these types of problems are usually studied for families of equal-size members. We will combine advanced probabilistic ideas to solve these problems for families containing graphs of all possible sizes. This has strong connections to ideas from statistical physics. In the second set of problems we investigate classical extremal graph theoretical problems in the context of random graphs. Roughly speaking, we start with a graph satisfying some property (either deterministically or typically), and we want to measure how many edges can be removed (either randomly or deterministically) until the property no longer holds. These types of problems are known as robustness, resilience, and Turan-type problems. Here we study these problems with respect to spanning structures. The experienced researcher has made several advances to these problems and to closely related problems. For example, she solved robustness and Turan-type problems for almost-spanning cycles (with Krivelevich and Mond), and she approximately solved the counting problem of directed Hamilton cycles (With Ferber and Long). The supervisor, Prof. Keevash, is a world leading expert on the absorption method, a key tool to approach extremal problems when considering large structures. A combination between these ideas with new probabilistic and statistical-physics tools, will be the key ingredient in this research.

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