Toky, cykly, plochy a polynomy

Název projektu anglicky
Flows, cycles, surfaces and polynomials
Anotace anglicky
Flows in graphs and the dual notion of tensions permeate combinatorial theory, not least because their definition extends from graphs to other combinatorial structures such as matroids and embedded graphs, and due to their applications in e.g. optimization and physics. Tantalizing conjectures abound -- Tutte's flow conjectures, snark conjectures, the cycle double cover -- and continue to exert a productive influence on the theory. The defining properties of tensions and flows in graphs involve cutsets and cycles, and the ways in which the edges of a graph can be covered by its cycles is closely related to the surfaces in which it embeds (the faces of a plane embedding of a bridgeless graph cover each edge exactly twice). To this interplay of flows, cycle covers, and surface embeddings we add randomness: we plan to establish a theory of random embeddings of graphs in surfaces, inspired by the success of the theory of random graphs. Connections to important conjectures on flows, cycles and polynomials will serve us both as a guide and a gauge for how useful our results are.

Kategorie VaV
ZV - Základní výzkum
OECD FORD - hlavní obor
10101 - Pure mathematics
OECD FORD - vedlejší obor
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OECD FORD - další vedlejší obor
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CEP - odpovídající obory <br>(dle <a href="http://www.vyzkum.cz/storage/att/E6EF7938F0E854BAE520AC119FB22E8D/Prevodnik_oboru_Frascati.pdf">převodníku</a>)
BA - Obecná matematika

Důvěrnost údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Systémové označení dodávky dat
CEP25-GA0-GA-R
Datum dodání záznamu
27. 2. 2025

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