|
|
||
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
|
|
||
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
The aim of the seminar is to make students of mathematics education acquainted with the basic notions and techniques of graph theory. On some selected themes the specific methods of argumentation and proofs in graph theory will be illustrated. The motivation by practical problems will be put into the foreground and the effectiveness of graph-theoretical methods will be shown. |
|
||
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
§ Vrba: Grafy - učebnice pro gymnázia se zaměřením na matematiku, SPN 1989 § Nešetřil: Teorie grafů, SNTL, Praha 1979 § Matoušek, Nešetřil: Kapitoly z Diskrétní Matematiky, Matfyzpress, Praha, 2000 § Sedláček: Úvod do teorie grafů Academia, Praha 1981, § Fuchs: Diskrétní matematika pro učitele MU Brno, 2001 |
|
||
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
At the seminar we will present standard problems and on the solution of these problems we will illustrate the fundamental notions and methods of graph theory. Thus a rather concrete approach, close to problem solving will be used.
|
|
||
Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)
Main topics: § Definition of the basic concepts (graph, complete graph, circle, path, tree). The score of a graph. § Connected graphs, distance in graphs, closed paths, Hamiltonian circle, Eulerian graphs. § Representations of a graph: matrix of neighbourhood, matrix of incidence. § Independence of a graph, the theory of coding. § Planar graphs, maps, graph colouring, the four colour problem. |