Graph Theory
Spring 2023

The Petersen graph labeled as a Kneser graph

STCs: JCC 270,   6:00-7:15pm

Instructor: Michael Jahn (Michael.Jahn@tufts.edu)

CA: Adam Xu (Adam.Xu@tufts.edu)

Office Hours:

Text: Introduction to Graph Theory, 2e, by Douglas West

Other texts you might look at:


HW, Handouts, etc.: will be posted at https://www.cs.tufts.edu/comp/150GT/documents/
and an archive of all the docs from class are archived here: https://www.cs.tufts.edu/comp/150GT/documents/CLASS-DOCS.pdf

Homework: PDF submission to Gradescope. LaTeX preferred. Please no scans of handwritten solutions.

Project: There is no required programming in this course. But your project may be an implementation, or it may be a theoretical project.

Guidelines for write-ups: On any HW or Project (even on an Exam, as much as possible) you should present your solution with your fellow students in mind as the audience, not me. Level-of-detail is determined by what your classmates need to see, in order to understand your solution without having to solve the problems for themselves.

Schedule by Lecture

Week 1
Wed, 18 Jan 2023
§1.1 intro/def of graphs
Week 2
Mon, 23 Jan 2023
§1.1 isomorphism
walks, trails, paths
Wed, 25 Jan 2023
§1.2 connected, cut-edge, closed odd walk contains odd cycle
indep set, bipartite graph, G bipartite iff no odd cycle
Week 3
Mon, 30 Jan 2023
Eulerian circuits
Handshaking lemma
Wed, 1 Feb 2023
§1.3 Counting cycles,
vertex deletions,
graphic sequences
Week 4
Mon, 6 Feb 2023
extremal problems,
trees and distance
Wed, 8 Feb 2023
§2.2, p.81 QUIZ 2
Prufer sequences (for counting labeled trees)
Week 5
Mon, 6 Feb 2023
§2.3, p.101
§2.2, p.87
Huffman codes
Graceful labeling
See also graceful-labeling-algorithms-and-complexity.pdf, and the standard reference on labeling, Gallian's ongoing survey (currently in its 25th edition). There's a link to the pdf on that page.
Wed, 15 Feb 2023
§2.1 QUIZ 3
distance, diameter, eccentricity, radius, center, Weiner index
Week 6
Mon, 20 Feb 2023 HOLIDAY (Presidents' Day)
Wed, 22 Feb 2023
§5.1 vertex colorings, χ(G), k-critical, α(G), ω(G), join, cartesian product
THU, 23 Feb 2023
Brooks' Theorem
The paper Brooks' Theorem and Beyond.pdf gives a proof of Brooks using Kempe-chains, along with several other proofs using different approaches.
Week 7
Mon, 27 Feb 2023 EXAM 1 (on material up through Feb 15 in class, Chapters 1, 2)
L 12
Wed, 1 Mar 2023
Mycielski's construction
χG(k) = chromatic polynomial (of a graph G)
Week 8
L 13
Mon, 6 Mar 2023
§6.1 Planar embeddings
L 14
Wed, 8 Mar 2023
§6.2 Euler's Theorem, subdivision, k-connectivity
Week 9
L 15
Mon, 13 Mar 2023
§6.2 Kuratowski's theorem
L 16
Wed, 15 Mar 2023
§6.3 QUIZ 4 (on HW 6)
Coloring planar graphs: 5-color Theorem (using Kempe-chains)
hw8.pdf (Not graded--do not turn in)
Week 10
Mon, 20 Mar 2023 SPRING
Wed, 22 Mar 2023 BREAK
Week 11
L 17
Mon, 27 Mar 2023
§7.1 Edge coloring
L 18
Wed, 29 Mar 2023
§7.2, 7.3 Vizing's Theorem
Hamiltonian Cycles
Week 11
L 19
Mon, 3 Apr 2023
Hamiltonian Cycles: Dirac's Theorem, Bondy-Chvatal
L 20
Wed, 5 Apr 2023
§3.1 QUIZ 5 (on HW 7 and 8)
Matchings: Hall's Theorem
Week 12
L 21
Mon, 10 Apr 2023
§3.1 Konig-Egervary Theorem
L 22
Wed, 12 Apr 2023
Connectivity, edge-connectivity
Network flows
Week 13
Mon, 17 Apr 2023 HOLIDAY (Patriot's Day)
L 23
Wed, 19 Apr 2023
snow day?
L 24
Fri, 21 Apr 2023
Algebraic graph theory, linear maps, eigenvalues, determinants
Week 14
L 25
Mon, 24 Apr 2023
Probabilistic method, random graph models
Wed, 26 Apr 2023 EXAM 2 (Note: not cumulative)
Fri, 28 Apr 2023 PROJECT DUE: report.pdf and slides.pdf
Week 15
Mon, 1 May 2023 Last day of class

PROJECT presentations   6:00-8:00pm
There will be pizza. And fabulous non-cash prizes!

Week 16
No Final Exam Yay!

Some important dates I got from Admin:

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