1 1/19We: introduction (overview of topics)

Chapter 6: Elementary Structural Concepts

2 1/21Fr: Matrix Tree Theorem, Matrix Arborescence Theorem, counting Eulerian circuits

3 1/24Mo: graceful labelings (hypercubes), T-decomposition (girth vs diameter)

4 1/26We: graph packing (Sauer-Spencer Thm, Bollobas-Eldridge Conj), graphic lists

5 1/28Fr: Aigner-Triesch for bigraphic lists, potentially k-edge-connected lists, vertex ptn for maximum degree

6 1/31Mo: vertex partition for minimum degree (Stiebitz), graph
reconstruction through Counting Theorem

7 2/02We: reconstruction of trees and almost all graphs,
edge-reconstruction

8 2/04Fr: isometric embedding & metric representation

9 2/07Mo: product dimension

Chapter 7: Connection and Cycles

10 2/09We: Edmonds' Branching Theorem and applications

11 2/11Fr: Lucchesi-Younger Theorem

12 2/14Mo: *k*-linked graphs, forced subdivisions

13 2/16We: ear decomposition, contraction lemma, 3-connected graphs, Halin example

14 2/18Fr: minimally *k*-connected graphs (Mader etc.), sketch of
Gyori-Lovasz Theorem

15 2/21Mo: Nash-Williams Orientation Theorem

16 2/23We: toughness (9/4-tough non-Hamiltonian), *k*-closure, density theorems

17 2/25Fr: Bondy-Chvatal condition for *t* dominating verts,
Las Vergnas condition, Lu's Theorem strengthening Chvatal-Erdos (skipping hard
case)

18 2/28Mo: Oberly-Sumner Theorem, Ryjacek closure (sketch), Erdos-Gallai
extremal result on circumference

19 3/02We: Bondy's Lemma on long paths, Fan's Theorem, Ghoula-Houri's Theorem

20 3/04Fr: Meyniel's Theorem (Bondy-Thomassen proof), gossip problem

Chapter 8: Planar and non-planar graphs

21 3/07Mo: MacLane/Whitney planarity criteria, Schnyder labelings and grid
embeddings

22 3/09We: Schnyder labelings (proofs)

23 3/11Fr: graph dimension, lemmas for Lipton-Tarjan Separator Theorem

24 3/14Mo: Lipton-Tarjan Separator Theorem, applications to independent sets
and pebbling

25 3/16We: Thomassen 3-colorability of planar graphs with girth at least 5

26 3/18Fr: Grotzsch's Theorem, Wernicke by discharging, reducibility of
Birkhoff diamond, Tait's Theorem

27 3/28Mo: interval number and total interval number of planar graphs

28 3/30We: thickness and pagenumber

29 4/01Fr: crossing number and application

30 4/04Mo: *t*-linear crossing numbers, genus, Heawood's Formula

31 4/06We: voltage graphs

Chapter 9: Graph minors and related topics

32 4/08Fr: graph minors, testing minors, *K _{4}*-minor-free
= 2-decomposable

33 4/11Mo: treewidth, cops-and-robber

34 4/13We: brambles, min/max for treewidth

35 4/15Fr: graph minor approach, well-quasi-ordering for trees (sketch)

36 4/18Mo: cycle covers and flows

37 4/20We: 8-flow theorem

38 4/22Fr: modular flows, 6-flow theorem

39 4/25Mo: snarks and faithful covers

Chapter 10: Algebraic graph theory

40 4/27We: eigenvalues (up to bipartite graphs)

41 4/29Fr: eigenvalues of regular graphs

42 5/02Mo: strongly regular graphs (Friendship Theorem), Laplacian eigvals

43 5/04Mo: chromatic polynomial, rank polynomial