Project description
Getting a handle on the randomness in random graphs
Random graphs are graphs for which certain properties including vertices, edges and the connections between them are determined in some random way. They have many applications in real-world networks including the World Wide Web, food webs, neural networks, social networks and power grids. Characterising and understanding the emergence of large structures and substructures in random graphs is a subject of particular interest. With the support of the Marie Skłodowska-Curie Actions programme, the LASTING project is investigating important problems in the realm of large structures in random graphs.
Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics applied mathematics statistics and probability
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) H2020-MSCA-IF-2020
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
OX1 2JD Oxford
United Kingdom
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.