Kevin Milans : Teaching : Fall 2014 Math573

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 1:30pm-2:30pm, Tues 11:30am-12:30pm, and by appointment
Class Meetings: MWF 12:30pm-1:20pm in Armstrong Hall 203
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Section(s) Comments
1 Aug 18 Introduction; Definitions 1.1 HW1 assigned.
2 Aug 20 Graph isomorphisms; more definitions 1.1 -
3 Aug 22 Petersen Graph; Walks, Trails, and Paths 1.1, 1.2 -
4 Aug 25 Walks, Cut-edges, Cut-vertices 1.2 -
5 Aug 27 Induced subgraphs; Cut-edges and cycles 1.2 -
6 Aug 29 Bipartite graph characterization 1.2 HW1 due; HW2 assigned.
7 Sep 3 Maximal vs. Maximum; Eulerian graphs 1.2 -
8 Sep 5 Eulerian graphs: sufficiency; Even graphs and cycle decompositions 1.2 -
9 Sep 8 Decomposition into trails; degree sum formula; hypercubes 1.2, 1.3 -
10 Sep 10 Extremal arguments and algorithmic proofs 1.3 -
11 Sep 12 Mantel's Theorem; Inductive trap 1.3 HW2 due; HW3 assigned.
12 Sep 15 Degree sequences; Havel-Hakimi Theorem 1.3 -
13 Sep 17 Directed graphs intro; De Bruijn cycles 1.4 -
14 Sep 19 Trees 2.1 -
15 Sep 22 Prufer Codes 2.2 -
16 Sep 24 Enumerating spanning trees; Deletion-contraction; Matrix Tree Thm 2.2 -
17 Sep 26 Matchings Intro 3.1 HW3 due; HW4 assigned.
18 Sep 29 Augmenting paths 3.1 -
19 Oct 1 Hall's Theorem 3.1 -
20 Oct 3 Midterm Exam - -
21 Oct 6 Konig--Egervary Theorem 3.1 -
22 Oct 8 Independent Sets and Covers 3.1 -
23 Oct 10 Ore's Theorem 3.3 HW4 due.
24 Oct 15 Vertex Connectivity 4.1 HW5 assigned.
25 Oct 17 Edge Connectivity 4.1 -
26 Oct 20 Vertex and Edge Connectivity; Blocks 4.1 -
27 Oct 22 Internally disjoint paths; Expansion Lemma 4.2 -
28 Oct 24 Subdivisions; Ear Decompositions 4.2 -
29 Oct 27 Closed Ear Decompositions; Local connectivity 4.2 -
30 Oct 29 Menger's Theorem 4.2 -
31 Oct 31 Flows I: Definitions, Augmenting paths 4.3 HW5 due; HW6 assigned.
32 Nov 3 Flows II: Cuts, Ford--Fulkerson 4.3 -
33 Nov 5 Flows III: Integrality, Applications 4.3 -
34 Nov 7 Graph coloring introduction 5.1 -
35 Nov 10 Cartesian product of graphs, greedy coloring 5.1 -
36 Nov 12 Class canceled - HW6 extended.
37 Nov 14 Interval graphs, orientations and chromatic number 5.1 -
38 Nov 17 Brooks's Theorem 5.1 -
39 Nov 19 Mycielski's construction 5.2 -
40 Nov 21 Turan's Theorem 5.2 HW6 due; HW7 assigned.
41 Dec 1 Hajos and Hadwiger conjectures; planar graphs intro 5.2, 6.1 -
42 Dec 3 Duals; outerplanar graphs 6.1 -
43 Dec 5 Euler's formula; regular polyhedra; Kuratowski's theorem 6.2 -
44 Dec 8 Chromatic number of planar graphs 6.3 HW7 due.
- Dec 12 Final Exam: 8am-10am - -
milans@math.wvu.edu