Applications of graphs and matrices

First, an introduction to graphs and their representation possibilities (e.g. by matrices) as well as some well-known graph-theoretical problems (e.g. Königsberg bridge problem, four-color problem) is given.

The lecture "Multi-stage processes" discusses problems in which an initial situation, which can be described by a state vector, is transformed into a subsequent situation with the help of transition matrices. The most important aspects are highlighted using detailed examples.

Many practical problems in everyday life (e.g. route planning) can be modeled and solved with the help of graphs. Some models and optimization methods for solving shortest path problems and round trip problems are presented. Finally, graph coloring problems are considered that have applications in timetabling and sports league planning.

Program

09.30 - 09.45Welcome
09.45 - 10.30Graphs: Introduction and some applications (Prof. Dr. S. Knust)
10.30 - 11.00Coffee break
11.00 - 12.15Multi-stage processes (Dr. H. Behnke)
12.15 - 13.30Lunch break
13.30 - 14.30Optimization methods for shortest path problems and round trip problems (Prof. Dr. S. Knust)
14.30 - 15.00Coffee break
15.00 - 16.00Graph coloring and its applications (Prof. Dr. S. Knust)
16.00 - 16.30Discussion and closing remarks