Grafentheorie en combinatoriek

This course introduces fundamental concepts, results and proof techniques in graph theory and combinatorics, including probabilistic, extremal, algebraic, and enumerative combinatorics. Applications and relationships between combinatorics and graph theory to other branches of math will be highlighted when present.
The course opens with a deep dive into graph theory. Graph theory forms the core of the course and provides a common setting for exploring broader combinatorial questions and techniques. The topics from this portion of the course include: basic notions of graphs, matchings and connectivity, coloring, the Probabilistic method, extremal graph theory including Ramsey theory.
The final part of the course explores selected topics in other branches of combinatorics: Possible topics include enumerative combinatorics, algebraic and linear algebraic methods, and combinatorial designs.

Learning goals
Upon successful completion of the course, students will be able to:

1. Use fundamental concepts and theorems from graph theory concerning graph structure, connectivity, matchings, coloring and Ramsey theory to analyze and solve combinatorial problems.
2. Construct and communicate rigorous proofs using inductive, enumerative, extremal, probabilistic and algebraic techniques.
3. Explain the key concepts from different areas of combinatorics, such as extremal combinatorics, enumerative combinatorics, algebraic combinatorics.
4. Explain connections between combinatorics and/or applications other areas of mathematics through selected results and examples.

Teaching Methods

Assessment

Resit and Effort Requirement

Language
English

Kansrekening (WISB161), Lineaire Algebra (WISB107 and WISB108), Bewijzen in de Wiskunde (WISB102)

• Book The opening part of the course follows selected chapters of J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. This book is available for free online via Universite de Montreal.
• Miscellaneous Additional material supports the remaining topics.