Graph Theory

What it is about

You learn the fundamentals of graph theory: paths and cycles, connectivity, trees, matchings, k-connectivity and Menger's theorem, as well as planar graphs and colorings. In the end you can apply central definitions and theorems, carry out proofs, and transfer the concepts presented to concrete problems and simple applications (including from data analysis).

What you will be able to do

• Understand and be able to explain the basic concepts of graph theory
• Apply matchings and stable matchings
• Apply k-connectivity and Menger's theorem
• Use properties of planar graphs and Kuratowski's theorem
• Apply graph colorings and chromatic number, including the Five Color Theorem
• Use adjacency, incidence and Laplacian matrices
• Recognize fundamental applications of graph theory in applied mathematics

What the module consists of

• VorlesungDelivery of theoretical fundamentals and proofs
• ÜbungSolving and discussion of exercises to reinforce and apply the material

Teaching method

• VorlesungPresentation of definitions, theorems and proofs
• Übungsaufgaben mit Einreichmöglichkeitfor practice, self-check and awarding a grade bonus for regular participation and submission