Subject: Discrete mathematics

Guarantee of the subject: Doc. RNDr. Eva Milková, Ph.D.

Time request: 2/2

Aims of the subject:

The aim is to develop and increase logical and algorithmic thinking of students, to make them familiar with the base of Combinatorics, Theory of Graphs and Combinatorial Algorithms.

Subject matter:

Combinatorics

• Basic combinatorial configurations

Theory of Graphs and Combinatorial Algorithms

• Basic concepts
• Trees and their properties
• The spanning tree, the number of spanning trees
• The minimum spanning tree problem
• Breadth_First _Search, Depth_First_Search
• Searching trees and their properties
• Modification of searching algorithms
• Eulerian graph
• Algorithm for finding an Eulerian trail
• Introduction to Hamiltonian and plane graphs

Obligatory literature

Milková, E.: Problém minimální kostry grafu, Gaudeamus, Hradec Králové, 2001

Milková, E: study material prepared in electronic form in the virtual study environment WebCT (https://oliva.uhk.cz)

Recommended literature

Calda E., Dupač V.: Matematika pro gymnázia: Kombinatorika a pravděpodobnost, Prometheus, Praha, 1995

Vilenkin, N. J.: Kombinatorika, SNTL Praha, 1977

Demel, J.: GRAFY a jejich aplikace, Academia, Praha, 2002

Matoušek, J.,Nešetřil, J.: Kapitoly z diskrétní matematiky, Karolinum, Praha, 2000