- Aug 22, Mon. course overview and logistics; Sec 6.1: Matrix Tree Thm; proof
- Aug 24, Wed. counting out-trees in a digraph; Matrix Arborenscence Thm; proof
- Aug 26, Fri. finished proof; one-to-many bijection between rooted in-trees and Eulerian circuits.
- Aug 29, Mon. BEST Thm; graph packing; examples; counting arguments
- Aug 31, Wed. Sauer-Spencer Thm; proof; sharpness; Bollobás-Eldridge-Catlin Conj; statement of Hajnal-Szemerédi Thm
- Sep 2, Fri. proof of Hajnal-Szemerédi Thm
Sep 5, Mon. Labor Day — no class.
- Sep 7, Wed. finished proof of Hajnal-Szemerédi Thm
- Sep 9, Fri. Sec 6.2: vertex degrees; Kleitman-Wang Lemma; Havel-Hakimi Thm; statement of Erdős-Gallai
- Sep 12, Mon. constructive proof of Erdős-Gallai; dominance order; graphic sequences form an ideal
- Sep 14, Wed. Aigner-Triesch method; Gale-Ryser thm
- Sep 16, Fri. potentially-graphic 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 2-basis and planarity
- Sep 21, Wed. using Euler's Formula to prove nonplanarity; abstract dual; Whitney thm; straight-line embeddings; barycentric coordinates
- Sep 23, Fri. barycentric representation gives a planar straight-line 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: 6-color thm; 5-color thm; overview of proof of 4-color thm; unavoidable configurations and reducibility; list coloring; example showing strict inequality of chromatic number and list-chromatic number
- Oct 3, Mon. No class.
- Oct 5, Wed. planar graphs are 5-choosable; discharging; prop by Franklin
- Oct 7, Fri. discharging example of Cranston; edge-choosability
- 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; 2-cell 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; K4-minor-free graphs; discussion of K5-minor-free graphs
- Oct 26, Wed. Guest lecturer Michael Ferrara of the University of Colorado Denver: degree conditions for H-linkages
- Oct 28, Fri. Lauren Keough: characterization of sharpness examples for Sauer-Spencer
- Oct 31, Mon. Sec 7.1: large average degree (or min degree) forces large complete subdivisions; definition of k-linked
- Nov 2, Wed. large connectivity implies k-linked; 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. cops-and-robber; grid;
- Nov 9, Wed. brambles; robber strategy using brambles; statement of min-max theorem; Sec 9.2: well-qasi-orders; 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 23-25, Wed-Fri. 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