1 1/17We: introduction (overview of topics)

2 1/19Fr: Matrix Tree Theorem, Matrix Arborescence Theorem

3 1/22Mo: counting Eulerian circuits, graceful labelings (hypercubes)

4 1/24We: tree decomposition, degree sequences

5 1/26Fr: CANCELED (Univ power failure)

6 1/29Mo: Erdos-Gallai sufficiency by Aigner-Triesch method, Edmonds characterization of potentially k-connected sequences

7 1/31We: threshold sequences, reconstruction problem (counting arguments,
parameters)

8 2/02Fr: reconstruction of trees and almost all graphs, edge-reconstruction

9 2/05Mo: isometric embedding

10 2/07We: metric representation, product dimension

11 2/09Fr: product dimension, forcibly *k*-connected sequences

12 2/12Mo: Edmonds' Branching Theorem

13 2/14We: Lucchesi-Younger, Thomassen contraction lemma

14 2/16Fr: Tutte 3-connected characterization, Halin minimal *k*-connected graphs

15 2/19Mo: Mader minimal *k*-connected graphs, motivate Gyori-Lovasz Theorem

16 2/21We: Gyori-Lovasz proof

17 2/23Fr: Nash-Williams Orientation Theorem

18 2/26Mo: Hamiltonian graphs (toughness, *k*-closure, Las Vergnas condition)

19 2/28We: Bondy-Chvatal condition for *t* dominating verts, Lu's Theorem (strengthening Chvatal-Erdos)

20 2/30Fr: Lu's Theorem (proof)

21 3/05Mo: Erdos-Woodall extremal result on circumference, Bondy's Lemma on long paths

22 3/07We: Fan's Theorem on Hamiltonian cycles, gossip problem

23 3/09Fr: planarity review: dual graphs, Euler's Formula, Kuratowski's Theorem

24 3/19Mo: Lipton-Tarjan Separator Theorem

25 3/21We: application of separator theorem (pebbling, independent sets)

26 3/23Fr: coloring of planar graphs (idea of discharging)

27 3/26Mo: reducibility of Birkhoff diamond, Thomassen proof of Grotzsch's Theorem (sketch)

28 3/28We: Borodin discharging argument for 3-coloring, start genus

29 3/30Fr: genus, Heawood's Formula

30 4/02Mo: voltage graphs

31 4/04We: thickness and pagenumber

32 4/06Fr: crossing number

33 4/09Mo: minors, begin treewidth

34 4/11We: treewidth characterizations, cops in helicopters

35 4/13Fr: graph minor approach, well-quasi-ordering

36 4/16Mo: cycle covers and flows

37 4/18We: 8-flow theorem

38 4/20Fr: modular flows, 6-flow theorem

39 4/23Mo: eigenvalues (up to interlacing)

40 4/25We: bounds on largest eigenvalue, eigenvalues of regular graphs

41 4/27Fr: eigenvalues and expanders, strongly regular graphs (Friendship Theorem)

42 4/30Mo: chromatic polynomial, with relation to rank and Tutte polynomials

43 5/04Fr: quasi-random graphs (sketch of equivalent properties)