Discrete Mathematics: Combinatorics; Graph Theory; Design Theory

34 Past PhD Students (click for details)

Past Masters Students

• 7 Master of Science Students (by thesis) and 36 Master of Applied Mathematics Students (by project)
  • Sangeetha Srinivasan won an AU Outstanding Master Student Award (2006).
  • Brandon Swan won an AU Outstanding Masters Thesis Award (2012)

Past Undergraduate Students

• Todd Smith, 2003-04 (1 paper written)
• Michael Tiemeyer 2005-06 (awarded one of 22 fellowships by Auburn University ($4,000 stipend); honorary mention for a student talk at the Twelfth International Conference on Statistics, Combinatorics, Mathematics and Applications ($100 prize); 1 paper written)

• 2 books published (with other authors)
  • Design Theory (2nd Edition; Taylor and Francis)
  • Coding Theory and Cryptography : The Essentials (2nd Edition; Marcel Dekker)
• 2 Journal Volumes published 
  • Discrete Mathematics (In honor of Curt Lindner), Guest Editor (with Dean Hoffman), 284 (2004).
  • Discrete Mathematics (In honor of Anthony Hilton), Guest Editor (with Lars Andersen), 309 (2009).
• 8 book chapters published
• over 190 research papers published or accepted

• 4 NSF research grants (individual), 1988 - 2000 (over $180,000).
• 2 ONR research grants (with 2 colleagues), 1995 - 2001 (over $300,000)
• Eisenhower Foundation grant with joint funding from NSF and AU Outreach, 2002-2003 (over $100,000).
• NCLB grant with joint NSF, Education Foundation of America and AU Outreach funding, 2003-2005 and 2006-07 (over $275,000).
• NSF MSP grant (with 5 other PIs), 2003-2008 (over $8,900,000, with a supplemental grant of $375,000).
• NSF MSP supplementary grant 2009-2012 ($25,000 taking graduate students for math outreach in Central Australia)
• NASA Project Director for the last 2.5 years, 2009-2013 ($499,000)
• NSF Collaborative Grant (with Universities of Memphis and Colorado at Denver) Promoting Success in Undergraduate Mathematics through Graduate Teacher Training, 2019-2023 (over $365,000).

• In 2012-2013 have helped run a program for 26 bright high school children who spend a week at Auburn University, interacting with faculty from math, chemistry, biology, physics and geology.
• I held an NSF grant to take 3 graduate students to Central Australia to design and run math two camps each year for 5^th to 9^th grade students in the middle of Australia, some of the participants being aboriginal children. The camps go from Friday to Sunday. I have done this for 4 years (2009-2012), the last 3 times with graduate students. The graduate students are a mix of PhD students in Math or Math Ed, the Math Ed students also being current teachers. I also run a workshop for teachers, letting my students do some of the teaching, and take the students to an aboriginal school where we have taught a class and interacted all day with the teachers and children. On returning to Auburn, we initiated a problem solving day for middle school teams where explanations of their answers was more important than speed. Graduate students are now running the upcoming second such event.
• Since 2001, I have conducted 5 summer workshops on ``Critical Thinking and Problem Solving", a Discrete Math Leadership Institute for K-8th Grade Teachers'' to work with teachers in high need areas of Alabama. Each workshop lasts from 5 to 8 days, and involves 3 follow-up meetings in the ensuing school year. Also involved in this project are master teachers, some from Alabama who have been through the program, others coming from places such as Arizona, Ohio, Rhode Island and Texas. Funding for the project has come from the Eisenhower Foundation, the NSF, the Educational Foundation of America, Auburn University, and the involved school districts. The program was developed at Rutgers University by Joe Rosenstein. For more information on this effort, see Discrete Math Institutes
• From 2003 to 2009 I was a PI on an NSF MSP to work with 15 local school districts spread over a 2500 square mile area, Tuskegee University, and both Math Ed and Math faculty, to develop an aligned math curriculum that meets both the new AL Math Content and the NCTM process and content standards. This is funded by a $9,361,840 grant from the NSF (I was one of 5 PIs) and a $100,000 internal grant from Auburn University Outreach and the Colleges of Education and Sciences and Mathematics. For more information on this effort, see Team Math

1. On completing partial latin squares with prescribed diagonals, Electronic J. Combinatorics, 29 (2022), P3.47 (with S. Baumann, L. D. Andersen and A. J. W. Hilton)
2. Embedding an edge-coloring of K(n^r; λ₁; λ₂) into a hamiltonian decomposition of K(n^r+2; λ₁; λ₂), J. Graph Theory, 93 (2019), 49-63 (with M. Demir).
3. On the Number of Rainbow Spanning Trees in Edge-Colored Complete Graphs, Discrete Math., 341 (2018), 2343-2352 (with H-L. Fu, Y-H Lo and K. Perry).
4. Extreme equitable block-colorings of C4-decompositions of K_v - F, Australasian J. Combinatorics, 71 (2018), 92-103 (with S. Li and E.B. Matson).
5. Fair 1-factorizations and fair holey 1-factorizations of complete multipartite graphs, Graphs and Combinatorics, 32 (2016), 1377 - 1388 (with A. Erzurumluoglu).
6. Large sets of wrapped K-K Hamilton cycle decompositions of complete bipartite 3-uniform hypergraphs, J. Combinatorial Designs, 23 (2015), 499 - 508 (with H. Zhao).
7. Path Decompositions of Kneser and Generalized Kneser Graphs, Canadian Math. Bulletin, 58 (2015), 610-619 (with T. Whitt).
8. Enclosings of λ-fold 5-cycle systems for u = 1, J. Combinatorial Designs, 22 (2014), 196-215 (with Asplund and Keranen). 
9. Embedding an Edge-colored K(a(p); λ, μ) into a Hamiltonian Decomposition of K(a(p+r); λ, μ), Graphs and Combinatorics, 29 (2013),747–755 (with Bahmanian).
10. Embedding factorizations for 3-uniform hypergraphs, J. Graph Theory, 73 (2013), 216–224 (with Bahmanian)