Matroid Theory Assignments
Fall 2026

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Readings and Problems

The readings are from

James Oxley, Matroid Theory, second edition, Oxford University Press, 2011, supplemented by the following published papers:

SG: Basics of signed graphs and their frame matroids: "Signed graphs".
SGGM: "Signed graphs and geometry". The half edges and loose edges should be treated (for matroid purposes, and for graph contraction) as negative loops and positive loops, respectively.
MuCh: "The Möbius function and the characteristic polynomial" is our main reference for enumeration using matroids.

Readings

Read these lightly first, then carefully.
Read and think about the recommended problems and hand-in problems.
Hand in the specified problems; I accept partial solutions and I don't expect you to answer every single one.
Extra problems, like definitions and explanations, are on a separate page.
There are occasional errors (big-ish to tiny) in the book. Check the corrections page often.

Weekly Assignments

Check the main page outline for exact readings.
Read every assigned problem, both recommended and hand-in. Even the ones you don't solve usually have useful information about matroids.
I do not expect you to solve all the problems. Solve as many as you can do a good job on. A few good solutions are worth much more than many bad solutions. Note that use of AI does not contribute to your learning (maybe the AI learns).

* = an especially important problem to learn, whether or not you solve it.

"P" problems are on the Project Page. "X" problems are on the Extra Page.

Boldface problems are the ones that were graded.

No. Week of: Reading: Recommended
problems: Hand in: Notes:

O All term: Oxley's Preliminaries It has essential background on finite fields and graphs that you should keep in mind.

A 8/19-8/21: §1.1 §1.1 10 (amusing). M 8/31 (rev'd): §1.1 #2, 5, 11; P1(a).

B 8/24-8/28: §§1.2-1.4 §1.1 #*14;
§1.2 ##*1, *2, *3, *5. W 9/2 (rev'd): P2, P3.
W 9/2: §1.1 ##4, 9; §1.2 ##2, 5; §1.3 ##1, 2.

C 8/31-9/4: §§1.5-7

C 9/8-9: §2.1 W 9/9: §1.4 ##3, 4.

D 9/14-18: §§2.2-3 §1.4 #*5, *6, *11; §1.5 #6, 15; §2.1 #*5. F 9/18: §1.3 #5; §1.4 #*5, 8; §2.1 #1(a), *10(a,b); §2.2 #1, 4. Omit clutters, m-partitions, spikes.

E 9/23-25: W: §3.1; F: §3.2-3 §1.7 #4. F 9/25: §1.3 #7; §1.4 #7, §1.5 #4. Note what §1.4 #7 is telling us about M*.
* How to think about contraction: Usually, use Prop. 3.1.6.

F 9/28-10/2: §4.1; begin SGGM §2.2 #2; §2.3 #2; §3.2 #2(c). F 10/2: §2.2 #*6; [§2.3 #8 postponed]; §3.1 #*1,*3. SGGM has information on switching (basic), coloring (more advanced), etc.

G 10/5-9: §4.2; Props. 4.3.1, 4.3.7-8; SGGM §§1, 2.0-2.5 §1.7 #7; §3.1 #17; §4.1 #*8. F 10/9: §2.2 #*7; §2.3 #8; §3.1 #8; §3.2 #11; 4.1#*1; P6. * See Oxley's correction of §2.3 #8.
* How would §4.1 #8 be stated if it said "inseparable" instead of "2-connected"?
* The SGGM reading is about basics of signed graphs and the frame matroid.

H 10/19-23: §§5.1-3;
SGGM §§3-4.1;
MuCh §7.5 "Chromatic poly." §4.1 #2; §5.2 #6, *7; §5.3 #2. F 10/23: P7; §4.2 #4, 7(a); §4.3 #1, *5; §5.1 #1, 3; §5.2 #*5; §5.3 #1(a). Representation of M(G), Prop. 5.2.7, and Whitney's 2-Isomorphism Theorem are essential. Omit transversal matroids, gammoids, spikes.
In SGGM, omit §3.5.2.

No.	Week of:	Reading:	Recommended problems:	Hand in:	Notes:
O	All term:	Oxley's Preliminaries			It has essential background on finite fields and graphs that you should keep in mind.
A	8/19-8/21:	§1.1	§1.1 10 (amusing).	M 8/31 (rev'd): §1.1 #2, 5, 11; P1(a).
B	8/24-8/28:	§§1.2-1.4	§1.1 #14; §1.2 ##1, 2, 3, *5.	W 9/2 (rev'd): P2, P3. W 9/2: §1.1 ##4, 9; §1.2 ##2, 5; §1.3 ##1, 2.
C	8/31-9/4:	§§1.5-7
C	9/8-9:	§2.1		W 9/9: §1.4 ##3, 4.
D	9/14-18:	§§2.2-3	§1.4 #5, 6, 11; §1.5 #6, 15; §2.1 #5.	F 9/18: §1.3 #5; §1.4 #5, 8; §2.1 #1(a), 10(a,b); §2.2 #1, 4.	Omit clutters, m-partitions, spikes.
E	9/23-25:	W: §3.1; F: §3.2-3	§1.7 #4.	F 9/25: §1.3 #7; §1.4 #7, §1.5 #4.	Note what §1.4 #7 is telling us about M. How to think about contraction: Usually, use Prop. 3.1.6.
F	9/28-10/2:	§4.1; begin SGGM	§2.2 #2; §2.3 #2; §3.2 #2(c).	F 10/2: §2.2 #6; [§2.3 #8 postponed]; §3.1 #1,*3.	SGGM has information on switching (basic), coloring (more advanced), etc.
G	10/5-9:	§4.2; Props. 4.3.1, 4.3.7-8; SGGM §§1, 2.0-2.5	§1.7 #7; §3.1 #17; §4.1 #*8.	F 10/9: §2.2 #7; §2.3 #8; §3.1 #8; §3.2 #11; 4.1#1; P6.	* See Oxley's correction of §2.3 #8. * How would §4.1 #8 be stated if it said "inseparable" instead of "2-connected"? * The SGGM reading is about basics of signed graphs and the frame matroid.
H	10/19-23:	§§5.1-3; SGGM §§3-4.1; MuCh §7.5 "Chromatic poly."	§4.1 #2; §5.2 #6, *7; §5.3 #2.	F 10/23: P7; §4.2 #4, 7(a); §4.3 #1, 5; §5.1 #1, 3; §5.2 #5; §5.3 #1(a).	Representation of M(G), Prop. 5.2.7, and Whitney's 2-Isomorphism Theorem are essential. Omit transversal matroids, gammoids, spikes. In SGGM, omit §3.5.2.

To the main course page | extra material | corrections page | project page

Matroid Theory AssignmentsFall 2026

Readings and Problems

Readings

Weekly Assignments

Matroid Theory Assignments
Fall 2026