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Nathan Bowler

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Lecture course "Graph Theory II", winter semester 2018/19

Exercise sheets

There will be one exercise sheet per week.

Here are the exercise sheets:

Sheet 1

Sheet 2

Sheet 3

Sheet 4

Sheet 5

Sheet 6

Sheet 7

Sheet 8

Sheet 9

Sheet 10

Sheet 11

Sheet 12

Sheet 13

Background material:

The course is based on the book `Graph Theory' by Reinhard Diestel, and builds on the course `Graph Theory I'.

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Log:

16.10.	Definition and basic properties of the cycle space and cut space [0.9.1, 0.9.2, 0.9.4]
18.10.	Duality between circuits and bonds; Tutte's theorem [0.9.3, 2.1.2, 2.1.3, 0.9.3, 0.9.5, 2.2.6]
23.20.	Various characterisations of planarity [3.5, 3.6]
25.10.	Tree packing and covering [1.4]
30.10.	The Erdős-Pósa theorem; introduction to flows [1.3, 5.1]
1.11.	Group-valued flows [5.3]
6.11.	k-flows for small k [5.4, 5.5.1]
8.11.	Flows and colourings; 6-flows [5.5.2, 5.5.6, 5.6]
13.11.	The structure theorem of Gallai and Edmonds [1.2.3]
15.11.	The theorem of Thomas and Wollan I [6.2.3, 2.5.4]
20.11.	The theorem of Thomas and Wollan II [2.5.3]
22.11.	The theorem of Erdős and Stone from the regularity lemma [6.1.2]
27.11.	Proof of the regularity lemma [7.4 in the English edition]
29.11.	The theorem of Chvátal, Rödl, Szemerédi and Trotter [6.4.2, 6.4.3, 7.2.2]
04.12.	The induced Ramsey theorem I [7.3.1-7.3.3]
06.12.	The induded Ramsey theorem II [second proof of 7.3.1]
11.12.	Third proof of the induced Ramsey theorem; Perfect graphs I [4.5.1,4.5.2]
13.12.	Perfect graphs II [4.5.3-4.5.6]
18.12.	The Erdős-Hajnal conjecture.
20.12.	Fleischner's theorem [8.3]
8.1.	Wellquasiorders and Kruskal's theorem [10.1,10.2]
10.1.	Tree decompositions [10.3]
15.1.	Brambles [10.4]
17.1.	Forbidden minors and the Erdős-Pósa property [10.6]
22.1.	The grid theorem I
24.1.	The grid theorem II