Constructing Knowledge in Graph Theory and Combinatorial Optimization within the multimedia application ‘Graphs’

Abstract: Multimedia applications together with individual approaches within the didactic process have substantially influenced education. They give teachers an excellent chance how to support not only demonstrating and visualizing the explained subject matter to be much clearer and comprehensible, but also enable them to prepare such study material for students that optimizes their study habits. The Theory of Graphs together with Combinatorial Optimization is a wonderful, practical discipline. On the one hand, there are many methods which can be used for solving the same problem, while on the other hand, using effective modifications of one algorithm, we can devise methods of solving various other tasks. To educate students in this area it is important to make them familiar with certain algorithms in contexts to be able to get deeper into each problem and entirely understand it. In the paper we present just a few ideas that have proved successful in teaching and learning this part of mathematics with a big support of the program ‘Graphs’, whose main purpose is a visual representation of basic graph-concepts and graph-algorithms using a coloring process on graphs created within the program