Algebraic, topological and combinatorial methods in the study of discrete structuresSupervisor: prof. RNDr. Jozef Širáň, DrSc.
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|Project description:||In the proposed project, we will investigate several important problems from Discrete Mathematics, all of them of interdisciplinary nature. Specifically, we will consider problems concerning graph colourings, flows on graphs, harmonic graph morphisms, extremal graphs and their relation to symmetry, highly symmetric graph embeddings into surfaces, coherent configurations, and strongly regular graphs. The interlinking of these specific problems will be considered on two levels. Methodologically, we will concentrate on the use of methods from algebra, linear algebra, geometry and topology with regard to our proposed problems. In terms of the actual objects of our investigation, we will combine a wide range of problems that often have surprisingly deep internal connections. To mention some specific problems, we will focus on the Lovasz conjecture for infinite classes of cubic Cayley graphs, constructions of strongly regular graphs for parameters for which the existence has not been settled, developing a combinatorial theory of harmonic functions, and many other problems.|
|Kind of project:||APVV - Všeobecná výzva ()|
|Department:||Department of Mathematics and Constructive Geometry (FCE)|
|Project status:||In process of execution|
|Project start date :||01. 07. 2016|
|Project close date:||30. 05. 2020|
|Number of workers in the project:||2|
|Number of official workers in the project:||0|