Graph Theory

Graph Theory, Spring 2024

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Class Info

Syllabus
Textbook: Introduction to Graph Theory (2nd Edition) by Douglas B. West
Meeting times: Monday and Thursday at 10-11:50am in Sage 4101
Last Class: April 22th

Course Instructor:
Prof. George M. Slota (gmslota@gmail.com)
Office Hours: Monday/Thursday at 2-3pm in 317 Lally
Webex: https://rensselaer.webex.com/meet/slotag

Teaching Assistant:
Hannah Powers (powerh@rpi.edu)
Office Hours: Monday/Thursday at 4-5pm virtually
Webex: https://rensselaer.webex.com/meet/powerh

Mentors:
Brandon McCusker (mccusb@rpi.edu)
Office Hours: Wednesday 8-9pm virtually
Webex: https://rensselaer.webex.com/meet/mccusb
All below hours will be in 127 Amos Eaton
Yuanyi Zhang (zhangy85@rpi.edu)
Office Hours: Tuesday at 4-6pm
Zijian Zhong (zhongz3@rpi.edu)
Office Hours: Friday at 4-6pm

Lecture Notes and Readings

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

Week	Date	Topic	Readings	Notes
1	8 Jan	Introduction to Graphs, Definitions	West ch. 1.1	Intro Slides \| Lecture 1 \| Notes \| Intro Code \| Test Graph \| Video
	11 Jan	Isomorphism, Subraphs	West ch. 1.1-1.2	Lecture 2 \| Notes \| Video
2	15 Jan	MLK Day: No class
	18 Jan	Decompositions, Walks, Induction	West ch. 1.2	Lecture 3 \| Notes \| Video
3	22 Jan	Proof Techniques, Eulerian Circuits	West ch. 1.3	Lecture 4 \| Notes \| Video
	25 Jan	Degrees, Graphic Sequences, Directed Graphs	West ch. 1.4	Lecture 5 \| Notes \| Video
4	29 Jan	Trees	West ch. 2.1	Lecture 6 \| Notes \| Bag o' Tricks \| Video
	1 Feb	Tree Enumeration and Graceful Graphs	West ch. 2.2	Lecture 7 \| Notes \| Video
5	5 Feb	Tree Algorithms	West ch. 2.3	Lecture 8 \| Notes \| Video
	8 Feb	Special Topic: PageRank		Lecture 9 \| Notes \| Code \| Data \| Video
6	12 Feb	Bipartite Matching	West ch. 3.1-3.2	Lecture 10 \| Notes \| Video
	15 Feb	General Matching, Covers, Independent Sets	West ch. 3.3	Lecture 11 \| Notes \| Video
7	1920 Feb	Connectivity (Note: Tuesday class)	West ch. 4.1	Lecture 12 \| Notes \| Video
	22 Feb	2-connectivity, Biconnectivity	West ch. 4.2	Lecture 13 \| Notes \| Video
8	26 Feb	In class review	West ch. 1-3	Practice Exam \| Solution \| Study Sheet \| Review
	29 Feb	In-class exam	West ch. 1-3	Midterm Solution
9	4 Mar	Spring Break
	7 Mar	Spring Break
10	11 Mar	k-connectivity	West ch. 4.2	Lecture 14 \| Notes \| Video
	13 Mar	Network flow	West ch. 4.3	Lecture 15 \| Notes \| Video
11	18 Mar	Vertex Coloring	West ch. 5.1	Lecture 16 \| Notes \| Video
	21 Mar	More Coloring	West ch. 5.2	Lecture 17 \| Notes \| Video
12	25 Mar	EVEN MORE COLORING, Perfect Graphs	West ch. 5.3	Lecture 18 \| Notes \| Video
	28 Mar	Planarity	West ch. 6.1	Lecture 19 \| Notes \| Video
13	1 Apr	Kuratowski's Theorem	West ch. 6.2	Lecture 20 \| Notes \| Video
	4 Apr	Coloring of Planar Graphs	West ch. 6.3	Lecture 21 \| Notes \| Video
14	8 Apr	No Class: Eclipse
	11 Apr	Line Graphs, Edge Coloring	West ch. 7.1	Lecture 22 \| Notes \| Video
15	15 Apr	Hamiltonian Graphs	West ch. 7.2	Lecture 23 \| Notes \| Video
	18 Apr	Random Graphs		Lecture 24 \| Notes \| Video
16	22 Apr	Final Review	West ch. 1-7	Practice Exam \| Solution \| Study Sheet \| Notes
	25 Apr	No class: Study Day
17	30 Apr	Final Exam	West ch. 1-7	11:30am in LOW 4050

Weekly Problems

WPs will be assigned most weeks, with some amount of class time designated to work on them. You can (and should!) work together on these problems. Late WPs will be accepted in accordance with the policy in the syllabus.

WP #	Due Date	WP	Solution
1	12 Jan	WP 1	Solution
2	22 Jan	WP 2	Solution
3	26 Jan	WP 3	Solution
4	2 Feb	WP 4	Solution
5	9 Feb	WP 5	Solution
6	16 Feb	WP 6	Solution
7	23 Feb	WP 7	Solution
8	15 Mar	WP 8	Solution
9	22 Mar	WP 9	Solution
10	29 Mar	WP 10	Solution
11	5 Apr	WP 11	Solution
12	19 Apr	WP 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.

HW #	Due Date	Homework	Solution
1	2 Feb	HW 1	Solution
2	16 Feb	HW 2	Solution
3	23 Feb	HW 3	Solution
4	22 Mar	HW 4	Solution
5	29 Mar	HW 5	Solution
6	12 Apr	HW 6	Solution
7	19 Apr	HW 7	Solution