# Combinatorics and Graph Theory II

### Lecture on Tuesday 14:00, S11

The tutorials will be led by Andreas
Feldmann on Thursday at 9:00 in S10.

This page will contain brief summaries of lectures with links to
relevant literature. See the syllabus
in SIS. The contents of the lecture will probably closely match last year's version.

#### Topics covered:

- 2. 10.: Characterisation of maximum matchings via augmenting
paths. Blossom contraction and its relationship to maximum matchings.
Edmonds' Blossom algorithm for finding a maximum matching
in a graph [Blo,T].
- 9. 10.: Tutte's theorem on perfect matchings, Petersen's theorem [D].
- 16. 10.: Lemma on contractible edge for 3-connected graphs,
Tutte's characterisation of 3-connectivity [D], Kuratowski's and
Wagner's theorem [D].

#### Literature:

[Ba] P. Bartlett: Chordal
graphs (pdf lecture notes)

[BCh] The Bondy
and Chvátal theorem

[Blo] The
Blossom Algorithm

[Bo] B. Bollobás: Modern Graph Theory

[D] R. Diestel: Graph Theory

[EKR] The
Erdős-Ko-Rado theorem

[HR] Y. Haimovitch, A. Raviv: Chordal
graphs (pdf slides)

[T] R. Tarjan: Sketchy
notes on [...] blossom algorithm for general matching

[W] H. Wilf: Generatingfunctionology