Objective
Graph theory is a relatively new branch of mathematics. Early sources of inspiration are Kirchhoff’s theory of electrical networks and the 4-color problem, both from the 19th century. In the 20th century graph theory was one of the most rapidly growing branches of mathematics with applications to theoretical computer science (design and analysis of algorithms), operations research (combinatorial optimization) and models in engineering and economics. The internet may be thought as a graph. There are also strong ties to geometry, topology, probability theory and logic.
The main subjects in the project are graphs in the plane and on higher surfaces, graph decomposition, the Tutte polynomial and the graph flow conjectures, and also combinatorial problems arising from differential geometry. The project is centered around applying new approaches to some classical problems in graph theory, in particular problems in chromatic graph theory and flow theory. In some sense these problems have an algebraic unification in the Tutte polynomial of two variables. The Tutte polynomial has as special valuations (fixing one of the variables) the chromatic polynomial (introduced in 1912 by Birkhoff) and the flow polynomial. More recently, the Tutte polynomial has also become of interest in statistical mechanics.
Among the specific problems to be investigated is Tutte’s 3-flow conjecture from the early 1970es, the problem if the flow polynomial can have arbitrarily large roots (motivated by Tutte’s 5-flow conjecture), the Merino-Welsh conjecture on the numbers of spanning trees, acyclic orientations and totally cyclic orientations, and Wegner’s conjecture from 1977 about squares of planar cubic graphs. We expect to get significant new insight (but not complete solutions) to the two notoriously hard flow conjectures of Tutte (both of which are also described in Wikipedia). We expect to almost solve the Merino-Welsh conjecture. We expect to completely solve the Wegner conjecture.
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 computer and information sciences computational science
- natural sciences physical sciences classical mechanics statistical mechanics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics applied mathematics statistics and probability
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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.
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.
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.
ERC-2012-ADG_20120216
See other projects for this call
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.
Host institution
2800 KONGENS LYNGBY
Denmark
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.