图论
The goal of this course is to give students an overview over the most fundamental concepts and results in modern graph theory.
讲师
本杰明·苏达科夫
日期
2022年09月22日 至 12月22日
网站
课程大纲
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
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
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.