Toky a cykly v grafech na plochách

Název projektu anglicky
Flows and cycles in graphs on surfaces
Anotace anglicky
Flows in graphs have a long and rich history in combinatorial theory. In his influential paper, Tutte introduced the concept of nowhere-zero flows motivated by the duality to graph colorings in plane graphs. Nowhere-zero flows rose to prominence in part due to their connections to other important topics such as the Cycle Double Cover conjecture and Berge–Fulkerson conjecture. The importance of the topic is further reinforced through algebraic connections, in particular through the Tutte polynomial which enumerates flows and relates them to other graph invariants when evaluated at suitable points. Much of the research into nowhere-zero flows is inspired by Tutte's insightful conjectures and focuses on general graphs. In this project, we investigate the topic of flows in graphs drawn on surfaces, motivated by applications in graph coloring and a possible approach towards the Cycle Double Cover conjecture. Moreover, we develop the algebraic connection via the study of the surface Tutte polynomial.

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
CEP24-GA0-GA-R
Datum dodání záznamu
19. 2. 2024

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