Graph Theory
The goal of this course is to give students an overview over the most fundamental concepts and results in modern graph theory.
Lecturer
Benjamin Sudakov
Date
25th September ~ 18th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 15:30 - 17:20 | Online | ZOOM 12 | 815 762 8413 | BIMSA |
Syllabus
· Basic notions: graphs, graph isomorphism, adjacency matrix, paths, cycles, connectivity
· Trees, spanning trees, Cayley's formula
· Vertex and edge connectivity, 2-connectivity, Mader's theorem, Menger's theorem
· Eulerian graphs, Hamilton cycle, Dirac's theorem
· Matchings, Hall's theorem, Kőnig's theorem, Tutte's condition
· Planar graphs, Euler's formula, basic non-planar graphs, platonic solids
· Graph colourings, greedy colourings, Brooks' theorem, 5-colourings of planar graphs, Gallai-Roy theorem
· Large girth and large chromatic number, edge colourings, Vizing's theorem, list colourings
· Matrix-tree theorem, Cauchy-Binet formula
· Hamiltonicity: Chvátal-Erdős theorem, Pósa's lemma, tournaments
· Ramsey theory
· Turán's theorem, Kővári-Sós-Turán theorem
· Trees, spanning trees, Cayley's formula
· Vertex and edge connectivity, 2-connectivity, Mader's theorem, Menger's theorem
· Eulerian graphs, Hamilton cycle, Dirac's theorem
· Matchings, Hall's theorem, Kőnig's theorem, Tutte's condition
· Planar graphs, Euler's formula, basic non-planar graphs, platonic solids
· Graph colourings, greedy colourings, Brooks' theorem, 5-colourings of planar graphs, Gallai-Roy theorem
· Large girth and large chromatic number, edge colourings, Vizing's theorem, list colourings
· Matrix-tree theorem, Cauchy-Binet formula
· Hamiltonicity: Chvátal-Erdős theorem, Pósa's lemma, tournaments
· Ramsey theory
· Turán's theorem, Kővári-Sós-Turán theorem
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Benny Sudakov received his PhD from Tel Aviv University in 1999. He had appointments in Princeton University, the Institute for Advanced Studies and in University of California at Los Angeles. Sudakov is currently professor of mathematics in ETH, Zurich. He is the recipient of a Sloan Fellowship, NSF CAREER Award, Humboldt Research Award, is Fellow of the American Math. Society and was invited speaker at the 2010 International Congress of Mathematicians. He authored more than 300 scientific publications and is on the editorial board of 14 research journals. His main scientific interests are combinatorics and its applications to other areas of mathematics and computer science.