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Record: Yes

Level: Graduate

Language: English

Abstract

The goal of this course is to give students an overview over the most fundamental concepts and results in modern graph theory.

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

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.

Lecturer Email: [email protected]

TA: Dr. Ruijie Xu, [email protected]