 Aug 22, Mon. course overview and logistics; Sec 6.1: Matrix Tree Thm; proof
 Aug 24, Wed. counting outtrees in a digraph; Matrix Arborenscence Thm; proof
 Aug 26, Fri. finished proof; onetomany bijection between rooted intrees and Eulerian circuits.
 Aug 29, Mon. BEST Thm; graph packing; examples; counting arguments
 Aug 31, Wed. SauerSpencer Thm; proof; sharpness; BollobásEldridgeCatlin Conj; statement of HajnalSzemerédi Thm
 Sep 2, Fri. proof of HajnalSzemerédi Thm
Sep 5, Mon. Labor Day — no class.
 Sep 7, Wed. finished proof of HajnalSzemerédi Thm
 Sep 9, Fri. Sec 6.2: vertex degrees; KleitmanWang Lemma; HavelHakimi Thm; statement of ErdősGallai
 Sep 12, Mon. constructive proof of ErdősGallai; dominance order; graphic sequences form an ideal
 Sep 14, Wed. AignerTriesch method; GaleRyser thm
 Sep 16, Fri. potentiallygraphic vs forcibly graphic; examples; Kundu thm;
Sec 8.1: Euler's Formula; statement of Kuratowski thm and Wagner thm; difference between subdivision and minor
 Sep 19, Mon. cycle space and bond space; equivalence of 2basis and planarity
 Sep 21, Wed. using Euler's Formula to prove nonplanarity; abstract dual; Whitney thm; straightline embeddings; barycentric coordinates
 Sep 23, Fri. barycentric representation gives a planar straightline embedding; Schnyder labelings; existence of contractible edges
 Sep 26, Mon. existence of Schnyder labelings; arise inductively; Uniform Angle Lemma
 Sep 28, Wed. proof of Uniform Angle Lemma; barycentric coordinates from Schnyder labeling; gives barycentric representation
 Sep 30, Fri. Sec 8.2: 6color thm; 5color thm; overview of proof of 4color thm; unavoidable configurations and reducibility; list coloring; example showing strict inequality of chromatic number and listchromatic number
 Oct 3, Mon. No class.
 Oct 5, Wed. planar graphs are 5choosable; discharging; prop by Franklin
 Oct 7, Fri. discharging example of Cranston; edgechoosability
 Oct 10, Mon. statement of Grötzsch's thm; reducible configurations (safe faces)
 Oct 12, Wed. configurations are unavoidable
 Oct 14, Fri. Sarah Behrens: more conditions for graphic sequences
Oct 17, Mon. Fall Break — no class.
 Oct 19, Wed. Sec 8.5: higher surfaces; genus; 2cell embeddings; Euler's formula
 Oct 21, Fri. edge bound; Heawood formula; Sec 9.1: minors and subdivisions; historical context
 Oct 24, Mon. Hadwiger and Hajóos conjectures; clique sums; K_{4}minorfree graphs; discussion of K_{5}minorfree graphs
 Oct 26, Wed. Guest lecturer Michael Ferrara of the University of Colorado Denver: degree conditions for Hlinkages
 Oct 28, Fri. Lauren Keough: characterization of sharpness examples for SauerSpencer
 Oct 31, Mon. Sec 7.1: large average degree (or min degree) forces large complete subdivisions; definition of klinked
 Nov 2, Wed. large connectivity implies klinked; Sec 9.1: definition of treewidth
 Nov 4, Fri. examples; upper bound of treewidth of nxn grid; relation to connectivity; equivalent formulations of treewidth
 Nov 7, Mon. copsandrobber; grid;
 Nov 9, Wed. brambles; robber strategy using brambles; statement of minmax theorem; Sec 9.2: wellqasiorders; structure of proof of Graph Minor Theorem
 Nov 11, Fri. Derrick Stolee: Ryjacek closure
 Nov 14, Mon. products and powers of WQOs are also WQO
 Nov 16, Wed. trees under the rooted topological minor order are WQO; Sec 10.3: extremal numbers; statement of Turán; statement of Erdős–Stone thm; Erdős–Simonovits thm
 Nov 18, Fri. Nora Youngs: precoloring extensions of graphs
 Nov 21, Mon. statement of Szemerédi Regulary Lemma; Embedding Lemma and proof
Nov 2325, WedFri. Thanksgiving Break — no class.
 Nov 28, Mon. finished proof of Embedding Lemma; proof of Erdős–Stone thm
 Nov 30, Wed. proof of Regularity Lemma
 Dec 2, Fri. No class.
 Dec 5, Mon. James Carraher: planar separators
 Dec 7, Wed. Jeremy Trageser: graphic sequences with small gaps
 Dec 9, Fri. Zach Roth: voltage graphs
