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## Nathan Bowler

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

#### Exercise sheets

There will be one exercise sheet per week.

Here are the exercise sheets:

#### Background material:

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

#### 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

 Impress 2019-01-29, Nathan Bowler