Graph Theory

Graph Theory, Spring 2023

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Class Info

Syllabus
Textbook: Introduction to Graph Theory (2nd Edition) by Douglas B. West
Meeting times: Monday and Thursday at 4:00p.m. EST
Last Class: April 24th

Course Instructor:
Prof. George M. Slota (gmslota@gmail.com)
Office Hours: Monday/Thursday at 6-7pm in 317 Lally and by appointment for virtual
Webex: https://rensselaer.webex.com/meet/slotag

Teaching Assistant:
Neha Keshan (keshan@rpi.edu)
Office Hours: Tuesdays 9-11am and Wednesday 8-9am, virtual
Webex: https://rensselaer.webex.com/meet/keshan

Mentors:
Nicholas Desmarais (desman@rpi.edu)
Office Hours: Monday 12-2pm and Wednesday 12-1pm, in 118 AE
Webex: https://rensselaer.webex.com/meet/desman
Megan Goulet (goulem2@rpi.edu)
Office Hours: Tuesday and Friday 12-1:30pm, in 118 AE
Webex: https://rensselaer.webex.com/meet/goulem2

Lecture Notes and Readings

Note: Class schedule subject to (and likely will) change.

Week	Date	Topic	Readings	Notes
1	9 Jan	Introduction to Graphs, Definitions	West ch. 1.1	Intro Slides \| Lecture 1 \| Notes \| Intro Code \| Test Graph \| Video
	12 Jan	Isomorphism, Subraphs	West ch. 1.1-1.2	Lecture 2 \| Notes \| Video
2	16 Jan	MLK Day: No class
	19 Jan	Decompositions, Walks, Induction	West ch. 1.2	Lecture 3 \| Notes \| Video
3	23 Jan	Eulerian Circuits, Degrees, Graphic Sequences	West ch. 1.3	Lecture 4 \| Notes \| Video
	26 Jan	Directed Graphs	West ch. 1.4	Lecture 5 \| Notes \| Video
4	30 Jan	Trees	West ch. 2.1	Lecture 6 \| Notes \| Bag o'Tricks \| Video
	2 Feb	Tree Enumeration and Graceful Graphs	West ch. 2.2	Lecture 7 \| Notes \| Video
5	6 Feb	Tree Algorithms	West ch. 2.3	Lecture 8 \| Notes \| Video
	9 Feb	Special Topic: PageRank		Lecture 9 \| Notes \| Code \| Data \| Video
6	13 Feb	Bipartite Matching	West ch. 3.1-3.2	Lecture 10 \| Notes \| Video
	16 Feb	General Matching, Covers, Independent Sets	West ch. 3.3	Lecture 11 \| Notes \| Video
7	21 Feb	Connectivity (Note: Tuesday class)	West ch. 4.1	Lecture 12 \| Notes \| Video
	23 Feb	2-connectivity, Biconnectivity	West ch. 4.2	Lecture 13 \| Notes \| Video
8	27 Feb	In class review	West ch. 1-3	Practice Exam \| Solution \| Study Sheet
	2 Mar	In-class exam	West ch. 1-3	Midterm Solution
9	6 Mar	Spring Break
	9 Mar	Spring Break
10	13 Mar	No Class
	16 Mar	k-connectivity	West ch. 4.2	Lecture 14 \| Notes \| Video
11	20 Mar	Network flow	West ch. 4.3	Lecture 15 \| Notes \| Video
	23 Mar	Vertex Coloring	West ch. 5.1	Lecture 16 \| Notes \| Video
12	27 Mar	More Coloring	West ch. 5.2	Lecture 17 \| Notes \| Video
	30 Mar	EVEN MORE COLORING, Perfect Graphs	West ch. 5.3	Lecture 18 \| Notes \| Video
13	3 Apr	Planarity	West ch. 6.1	Lecture 19 \| Notes \| Video
	6 Apr	Kuratowski's Theorem	West ch. 6.2	Lecture 20 \| Notes \| Video
14	10 Apr	Coloring of Planar Graphs	West ch. 6.3	Lecture 21 \| Notes \| Video
	13 Apr	Line Graphs, Edge Coloring	West ch. 7.1	Lecture 22 \| Notes \| Video
15	17 Apr	More Line Graphs	West ch. 7.1	Notes
	20 Apr	Hamiltonian Graphs	West ch. 7.2	Lecture 23 \| Notes \| Video
16	24 Apr	Final Review	West ch. 1-7	Practice Exam \| Solution \| Study Sheet
	27 Apr	Study Day: No class
17	3 May	Final Exam	West ch. 1-7	Wednesday, 6:30-9:30PM in LOW 4050

Quizzes

Quizzes will be assigned most weeks. Quizzes will be assigned and due in class. You can (and should!) work together on quizzes. Late quizzes will NOT be accepted in accordance with the policy in the syllabus.

Quiz #	Date	Quiz	Solution
1	12 Jan	Quiz 1	Solution
2	19 Jan	Quiz 2	Solution
3	26 Jan	Quiz 3	Solution
4	2 Feb	Quiz 4	Solution
5	11 Feb	Quiz 5	Solution
6	16 Feb	Quiz 6	Solution
7	23 Feb	Quiz 7	Solution
8	20 Mar	Quiz 8	Solution
9	23 Mar	Quiz 9	Solution
10	30 Mar	Quiz 10	Solution
11	6 Apr	Quiz 11	Solution
12	13 Apr	Quiz 12	Solution

Homework

Homeworks due at MIDNIGHT EST on the due date. Collaboration is allowed on homeworks, but you must do your own work. Late homeworks will be accepted in accordance with the policy in the syllabus: 3 late days total with a max of one late day per assignment.

HW #	Due Date	Homework	Solution
1	6 Feb	HW 1	Solution
2	18 Feb	HW 2	Solution
3	25 Feb	HW 3	Solution
4	25 Mar	HW 4	Solution
5	8 Apr	HW 5	Solution
6	15 Apr	HW 6	Solution
7	22 Apr	HW 7	Solution