Oct 18, 2019   5:54 a.m. Lukáš
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Algebraic, topological, and combinatorial methods in discrete structures

Supervisor: prof. RNDr. Jozef Širáň, DrSc.


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Project description:In our proposed project, we focus on the relations between algebraic, combinatorial, and topological structures on graphs and other discrete structures. Our main interest is in the interplay between graph colourings, symmetries and embeddings of graphs, and nowhere-zero flows. All of these areas are essential parts of the contemporary discrete mathematics with deep connections to classical mathematical areas as well as immediate applications. Nowhere-zero flows constitute one of the traditional methods of graph colourings. The study of snarks belong to this area too. Regular maps play a prominent role in the study of symmetries of graphs and surfaces. We will focus, in particular, on maps with a vertex-regular subgroup of automorphisms - Cayley maps. The contribution of the Slovak mathematical community in the above areas, including the Slovak school of topological graph theory, is internationally recognized. The goal of this project is a continuation of this success - a creation of a strong vertical team consisiting of experienced researchers mixed with researchers at the beginning of their careers and graduate students that will guarantee the continuity of such results for the future. We also plan to cooperate with the Bratislava graph theory seminar and organize the international conference GEMS 2013 which traditionally covers the areas of our proposal.
Kind of project:APVV - Všeobecná výzva ()
Department:Department of Mathematics and Constructive Geometry (FCE)
Project identification:APVV-0223-10
Project status:Successfully completed
Project start date :01. 05. 2011
Project close date:31. 10. 2014
Number of workers in the project:2
Number of official workers in the project:0