Topics and Prerequisites
Final Exam and Requirements
|Arnimallee 3, Rm 207|
|firstname.lastname at gmail.com|
|Lectures will take place in Takustr 9, Room 46, on Tuesdays from 14:15 to 15:45.
Exercise classes will take place in Takustr 9, Room 55, on Wednesdays from 14:15 to 15:45.
On the first week, the exercise class will be replaced with a second lecture.
| Topics include: Graph Minor Theory: Tutte's lemma: generating 3-connected graphs; Kuratowski theorem: characterization of planar graphs; Mader's theorem: every graph with large average degree has a large clique minor; treewidth, brambles and tangles: treewidth duality theorem; excluded grid theorem; 2-disjoint rooted paths problem and Seymour's theorem; graph minor theorem for surfaces; statement(s) of the graph minor theorem. Sparsity: classes with bounded expansion; nowhere dense classes; characterisations, examples, current research.
|Discrete Mathematics I or equivalent (basic combinatorics and graph theory).|
|BMS: advanced course; FU Master: Discrete Mathematics III modul or Ergäzungsmodul.|
Homework assignments will be posted below, and should be submitted before 8:00am of the due day.
|Sheet 4 (updated 25/11 15:45)||30/11/2016|
|Sheet 6 (Diestel's paper [pdf])||14/12/2016|
|Sheet 7 (a survey about tangles by Martin Grohe [pdf]; Graph Minors X by Neil Robertson and Paul Seymour[pdf])||18/01/2017|
|Sheet 8 (here are the videos of the series of lectures that I am following with you these days)||25/01/2017|
|for the "Sheet 9", please watch Lecture 7 by Jim Geelen (Oct 3, 2016) and read section 12.5 of Diestel's book (5th edition!); among other things Geelen states an upgrade of the Grid Theorem: "A grid from a tange" or more precisely the theorem given around '35. As an exercise write down a sketch of the proof. As the second exercise I want you to understand the statement of the Tangle-Tree Theorem given at the same lecture and its proof given by Diestel. Is it the same proof as the one sketched by Geelen? I'm not sure ...||01/02/2017|