CV

Sarah Allred

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Employment

2023–Present Assistant Professor, University of South Alabama
2022–2023 Postdoctoral Scholar, Vanderbilt University

Education

2017–2022 Ph.D., Mathematics, Louisiana State University
Advisor: Bogdan Oporowski
Dissertation: Unavoidable Structures in Large and Infinite Graphs
2016–2017 M.S., Mathematics, Louisiana State University
2012–2016 B.S., Mathematics, Auburn University

Research Interests

General: Combinatorics, Graph Theory
Specific: Structural and Extremal Graph Theory

Papers

Published Papers

  1. S. Allred, P. Johnson, M. Murphy, Forbidding Rainbow Cycles with Edge-Colorings of Km,n. Alabama Journal of Mathematics Vol. 38 (2014).
  2. S. Allred, P. Johnson, Theta Graphs are Hall t-chromatic for all t = 0, 1, 2, … . Bulletin of the ICA, Vol. 81 (2017).
  3. S. Allred, G. Ding, B. Oporowski, Unavoidable Induced Subgraphs of Large 2-Connected Graphs. SIAM Journal of Discrete Mathematics, Vol. 37, Iss. 2 (2023).
  4. S. Allred, E. Curl, S. Fallat, S. Nasserasr, H. Schuerger, R.R. Villagrán, P.K. Vishwakarma, The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions.  Graphs and Combinatorics. Vol. 40, Iss. 2 (2024). 
  5. S. Allred, G. Ding, B. Oporowski, Unavoidable Induced Subgraphs of Infinite 2-Connected Graphs. Discrete Mathematics, Vol. 348, Iss. 4 (2025).
  6. S. Allred, C. Erickson, K. Grace, H.T. Hall, A. Jensen, A Combinatorial Bound on the Number of Distinct Eigenvalues of a Graph.  The Australasian Journal of Combinatorics, Vol. 91 Part 1 (2025).

Preprints

  1. S. Allred, M. N. Ellingham, Unavoidable Induced Subgraphs of 2-edge-connected graphs, submitted, arxiv: 2503.21574.
  2. S. Allred, J. A. Mudrock, Enumerative Chromatic Choosability. arXiv: 2505.05662.
  3. S. Allred, M. N. Ellingham, Forbidding the subdivided claw. arXiv: 2510.13718.

Papers in Preparation

  1. S. Allred, M. N. Ellingham, Vertex-Contraction-Deletion Minors.
  2. S. Allred, M.N. Ellingham, G. Zvaneweld. Adding odd holes to chordal graphs.

Extended Research Travel

Summer 2021 AMS Mathematics Research Community

Internships

Summer 2020

Software Engineering Institute, Carnegie Mellon University

  • Participated in ongoing research into investigating alterations to compressed archives:
    • Developed a prototype framework for format specifications
    • Represented data at multiple layers of abstraction, from binary encoding to human-readable description
  • Work product consisted of:
    • A series of technical presentations to a group with interests that include digital forensics, network security, and machine vision
    • A binary file parsing code in Python to read data and construct a higher-order representation of the file data

Honors, Awards, Distinctions

Louisiana State University

Fall 2020 Certificate of Teaching Excellence
Spring 2020 David Oxley Graduate Teaching Award
2016–2018 Board of Regents Fellow

Presentations

Invited Talks

2025 Unavoidable Structures in Large and Infinite Graphs,  KdVI DMQI Seminar, University of Amsterdam.
2025 Vertex Contraction-Deletion Minors, Georgia State Discrete Mathematics Seminar, Georgia State University.
2024 Unavoidable Structures in Large and Infinite Graphs, Trojan Math Seminar, Troy University.
2024 Enumerative Chromatic Choosability, IIT Discrete Mathematics Seminar, Illinois Institute of Technology.
2024 Vertex Contraction-Deletion Minors, University of Mississippi Combinatorics Mathematics Seminar, University of Mississippi.
2023 Unavoidable Induced Subgraphs of 2-connected Graphs, Georgia Tech Graph Theory Seminar, Georgia Institute of Technology.
2023 Unavoidable Induced Subgraphs of Infinite 2-connected Graphs, AMS Spring Southeastern Section Meeting, Georgia Institute of Technology.
2023 Unavoidable Induced Subgraphs of Infinite 2-connected Graphs, Joint Mathematics Meetings, Boston, MA.
2022 Unavoidable Induced Subgraphs of Large 2-connected Graphs, Auburn Combinatorics Seminar, Auburn University.
2022 Unavoidable Induced Subgraphs of Large and Infinite 2-connected Graphs, Joint Vanderbilt/MTSU Graph Theory and Combinatorics Seminar, Vanderbilt University.
2022 Unavoidable Induced Subgraphs of Large and Infinite 2-connected Graphs, Virtual Women in Combinatorics Seminar.
2022 Unavoidable Induced Subgraphs of Large 2-connected Graphs, Joint Mathematics Meetings.
2020 Unavoidable Induced Subgraphs of Large 2-connected Graphs, Graphs and Matroids Seminar, University of Waterloo.
2018 Theta Graphs are Hall t-Chromatic, Auburn REU, Auburn University.

Other Talks

2025 Unavoidable Induced Subgraphs of Large Graphs,39th Summer Conference on Topology and Its Applications, University of South Alabama.
2024 Forbidding the Subdivided Claw,33rd Cumberland Conference on Combinatorics, Graph Theory and Computing, Mississippi State University.
2022 Unavoidable Induced Subgraphs of Large and Infinite 2-connected Graphs, LSU Combinatorics Seminar, Louisiana State University.
2020 Unavoidable Induced Subgraphs of Large 2-connected Graphs, LSU Combinatorics Seminar, Louisiana State University.
2019 Unavoidable Induced Subgraphs of Large 2-connected Graphs, 7th Mississippi Discrete Math Workshop, University of Mississippi.
2019 Unavoidable Induced Subgraphs of Large 2-connected Graphs, 31st Cumberland Conference on Combinatorics, Graph Theory and Computing, University of Central Florida.
2018 Combinatorics Introduction Talk, GEAUX Program, Louisiana State University.
2018 Theta Graphs are Hall t-chromatic, 49th Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University.

Teaching

I was the instructor of record, with sole responsibility for preparing and presenting lectures, assigning and grading tests, and determining the overall course grade for the following courses.

University of South Alabama

Course Semesters
Graph Theory Sp2024, Sp2025
Discrete Math Structures Fa23, Sp24, Fa24, Sp25
Calculus I Fa24
Calculus II Su24
Finite Mathematics Fa2023

Vanderbilt University

Course Semesters
Methods of Linear Algebra Sp23
Error-Correcting Codes and Cryptography Fa22, Sp23

Louisiana State University

Course Semesters
Honors Calculus I Fa2020, Fa2021
Honors Calculus II Sp2021
Calculus I Sp2019, Fa2019
Calculus II Su2019
Differential Calculus Su2021
College Algebra Sp2020

Service and Outreach

Professional Service

Referee Discrete Mathematics Journal
  Banff International Research Station Workshop Proposal

University of South Alabama

Fall 2025–Present Board of Directors and Finance Committee Member, USA Wesley Foundation.
Summer 2024 Instructor, Math Corps.
Spring 2024 Plenary Speaker, Girls in Math Day at the University of South Alabama.
Fall 2023–Present Member, Graduate Committee.

Vanderbilt University

2023 Math Tutor, Community Achieves at H.G. Hill Middle School.

Louisiana State University

2021–2022 Member, Student Colloquium Committee, Louisiana State University.
2021 Chair, G.E.A.U.X Orientation Program for New Math Graduate Students, Louisiana State University.
2020–2022 Organizer, LSU Combinatorics Seminar, Louisiana State University: Organized and ran the LSU Combinatorics Seminar as a virtual seminar with participants from multiple countries.
Fall 2020 Mathematics Graduate Student Mentor Program, I started a tiered mentoring program for mathematics graduate students, pairing first-year graduate students with more advanced students for support.
Fa19, Sp20, Sp21, F21 Mentor for the Communicating Math Graduate Course, I mentored a first-year graduate student. I met with the student several times throughout the semester as they observed my class, and guided them through writing and presenting a lecture in my Calculus I course. Louisiana State University.
2019–2022 Department Representative to the Graduate Student Association, I represented the mathematics graduate students in the Graduate Student Association and presented any concerns graduate students had to the GSA. Louisiana State University.
2019 Math with Middle and High Schoolers,  I gave a talk on assorted topics in Graph Theory to both a middle school and a high school math class. Lafayette Christian School.
2017–2020 Committee Member, G.E.A.U.X Orientation Program for New Math Graduate Students, Louisiana State University.
2017–2022 Mentor, KIDS HOPE Mentored an elementary student in reading, mathematics, and life skills.
2017 Proctor and Grader, High School Math Contest, Louisiana State University.

Professional Memberships

American Mathematical Society
Association for Women in Mathematics

Last Updated: November 2025