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REU Result​​s

Single-Starred (*) authors are Undergraduate Participants,
Double-Starred (**) authors are In-Service Participants,
Triple-Starred (***) authors are Graduate Assistant Participants,
Quadruple-Starred (****) authors are high school student participants.

Completed Projects

  1. R. C. Bunge**, S. I. El-Zanati, W. O'Hanlon***, and C. Vanden Eyden, On gamma-labeling the almost bipartite graph Pm+e, Ars Combinatoria, Vol. 10​7 (2012), 65–80. [Download a pdf​]
  2. S. I. El-Zanati, K. King*, and J. Mudrock*, On the cyclic decomposition of circulant graphs into almost-bipartite graphs, Australasian Journal of Combinatorics, Vol. 49 (2011), 61–76. [Download a pdf]
  3. R. C. Bunge**, S. I. El-Zanati, M. Hirsch*, D. Klope*, J. A. Mudrock*, K. Sebesta**, and B. Shafer**, On labeling 2-regular graphs where the number of odd components is at most 2, Utilitas Mathematica, Vol. 91 (2013), 261–285. [Download a pdf]
  4. R. C. Bunge**, S. I. El-Zanati, C. Vanden Eynden, and C. Rumsey***, On the cyclic decomposition of circulant graphs into bipartite graphs, Australasian Journal of Combinatorics, Vol. 56 (2013), 201–217. [Download a pdf]
  5. S. I. El-Zanati and D. I. Gannon*, On rho-labeling 2-regular graphs consisting of 5-cycles, International Journal of Mathematics and Computer Science, Vol. 6 (2011), 13–20. [Download a pdf]
  6. S. I. El-Zanati and D. I. Gannon*, All 2-regular graphs with uniform odd components admit rho-labelings, Australasian Journal of Combinatorics, Vol. 53 (2012), 207–219. [Download a pdf]
  7. R. C. Bunge**, A. Chantasartrassmee, S. I. El-Zanati, and C. Vanden Eynden, On cyclic decompositions of complete graphs into tripartite graphs, Journal of Graph Theory, Vol. 72 (2013), 90–111. [Download a pdf]
  8. K. Brewington*, R. C. Bunge**, L. J. Cross**, S. I. El-Zanati, C. K. Pawlak*, J. L. Smith*, and S. M. Zeppetello*, On G-designs, where G is the one-point union of two cycles, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 83 (2012), 261–289. [Download a pdf]
  9. R. C. Bunge**, C. K. Pawlak*, J. L. Smith*, and S. M. Zeppetello*, Labelings of comets plus an edge, Proceedings of the Forty-Second Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, Vol. 209 (2011), 101–110. [Download a pdf]
  10. R. C. Bunge***, S. I. El-Zanati, A. Hakes*, J. Jeffries*, E. Mastalio*, and J. Torf*, On decomposing lambda-fold complete graphs into the standard Stanton 4-cycle, Proceedings of the Forty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congressus Numeratium, Vol. 215 (2013), 7–16. [Download a pdf]
  11. R. C. Bunge***, S. I. El-Zanati, D. Gibson*, U. Jongthawonwuth, J. Nagel*, B. Stanley*, and A. Zale*, On cyclic decompositions of Kn+1,n+1-I into a 2-regular bipartite graph with at most 2 components, Proceedings of the Forty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congressus Numeratium, Vol. 218 (2013), 73–84. [Download a pdf]
  12. S. I. El-Zanati, M. Ermete*, J. Hasty**, M. J. Plantholt, and S. K. Tipnis, On decompositions of regular graphs into double-stars, Discussiones Mathematicae Graph Theory, Vol. 35 (2015), 73–79. [Download a pdf]
  13. J. Buchanan*, R. C. Bunge***, E. Pelttari*, G. Rasmuson**, A. Su****, and S. Tagaris*, On decompositions of complete multipartite graphs into the union of two even cycles, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 96 (2016), 129–157. [Download a pdf]
  14. S. Allen*, J. Bolt**, R. C. Bunge***, S. Burton*, and S. I. El-Zanati, On the index 2 spectra of bipartite subgraphs of 2K4, Bulletin of the Institute for Combinatorics & its Applications, Vol. 74 (2015), 25–36. [Download a pdf]
  15. A. Arias*, R. C. Bunge, M. Carmona Herrera*, S. I. El-Zanati, U. Jongthawonwuth, and E. Sparks**, On cyclic decompositions of Kn-1,n-1+I into a 2-regular bipartite graph of size n and at most 2 components, Congressus Numerantium, Vol. 222 (2014), 21–32. [Download a pdf]
  16. R. C. Bunge, S. I. El-Zanati, J. Klister*, D. Roberts, and K. Ruddell*, On ordered directed rho-labelings of bipartite digraphs and cyclic digraph decompositions, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 99 (2016), 255–268. [Download a pdf]
  17. R. C. Bunge, S. I. El-Zanati, H.  J. Fry, K. S. Krauss*, D. Roberts, C. A. Sullivan*, A. A. Unsicker*, and N. E. Witt**, On the spectra of bipartite directed subgraphs of K4*, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 98 (2016), 375–390. [Download a pdf]
  18. S. R. Allen**, R. C. Bunge, E. Doebel*, S. I. El-Zanati, P. Kilgus*, C. Shinners*, and S. M. Zeppetello**, On the lambda-fold spectra for bipartite subgraphs of 2K4, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 101 (2017), 213–222. [Download a pdf]
  19. R. C. Bunge, C. J. Cowan*, L. J. Cross**, S. I. El-Zanati, A. E. Hart*, D. Roberts, ​and A. M. Youngblood*, Decompositions of Complete Digraphs into Small Tripartite Digraphs, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 102 (2017), 375–390. [Download a pdf]
  20. S. I. El-Zanati, M. Kopp*, M. J. Plantholt, and S. Rice*, On decomposing regular graphs into star forests, International Journal of Mathematics and Computer Science, Vol. 11 (2016), 249–256. [Download a pdf]
  21. R. C. Bunge, S. I. El-Zanati, L. Febles Miranda*, J. Guadarrama*, D. Roberts, E. Song**, and A. Zale**, On the lambda-fold spectra of tripartite multigraphs of order 4 and size 5, Ars Combinatoria, to appear.
  22. R. C. Bunge, S. I. El-Zanati, J. Mudrock*, C. Vanden Eynden, and W. Wannasit, On lambda-fold Rosa-type labelings of bipartite multigraphs, Electronic Notes in Discrete Mathematics, Vol. 60 (2017), 11–23.
  23. R. C. Bunge, S. DeShong*, S. I. El-Zanati, A. Fischer**, D. P. Roberts, and L. Teng*, The spectrum problem for digraphs of order 4 and size 5, Opuscula Mathematica, Vol. 38 (2018), no. 1, 15–30.
  24. N. A. Avila Cervantes*, R. C. Bunge, H. R. Bush*, D. P. Roberts, A. E. Rocha*, and K. M. Stilson**, Spectrum for multigraph designs on four vertices and six edges, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 106 (2018), 69–81.
  25. R. C. Bunge, J. Jeffries**, J. Kirkpatrick*, D. P. Roberts, and A. Sickman*, Spectrum for multigraph designs on four vertices and six edges, Congressus Numerantium, Vol. 228 (2017), 29–49.
  26. L. Cross**, E. Morales*, D. P. Roberts, and K. Stilson*, On cyclic decompositions of some complete direcetd graphs into antidirected cycles, Congressus Numerantium, Vol. 229 (2017), 361–377.
  27. R. C. Bunge, B. D. Darrow, Jr*, T. M. Dubczuk*, S. I. El-Zanati, H. H. Hao****, G. L. Keller**, and G. A. Newkirk*, On decomposing the complete symmetric digraph into orientations of K4-e, Discussiones Mathematicae Graph Theory, to appear.
  28. P. Adams, C. Chan*, S. I. El-Zanati, E. Holdaway*, U. Odabasi, and J. Ward*, The Spectrum Problem for 3 of the Cubic Graphs of Order 10, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.
  29. R. C. Bunge, S. I. El-Zanati, J. Jeffries**, and C. Vanden Eynden, Edge Orbits and Cyclic and r-Pyramidal Decompositions of Complete Uniform Hypergraphs, Discrete Mathematics, Vol. 341 (2018), no. 12, 3348–3354.
  30. R. C. Bunge, M. K. Chwee**, A. M. Cooper*, S. I. El-Zanati, K. L. Kennedy*, D. P. Roberts, and C. C. Wilson*, The spectrum problem for a multigraph on 4 vertices and 7 edges, Congressus Numerantium, to appear.
  31. R. C. Bunge, S. I. El-Zanati, D. J. Gibson**, D. P. Roberts, A. L. Sickman*, L. A. States*, and J. T. Ward*, The lambda-fold spectrum problem for a multigraph on four vertices and eight edges, Congressus Numerantium, to appear.
  32. R. C. Bunge, S. I. El-Zanati, K. A. Hawken*, E. Ramirez*, D. P. Roberts, E. Rodriguez-Guzman**, and J. D. Williams*, The spectrum problem for some digraphs of order 4 and size 6, submitted.
  33. R. C. Bunge, M. Cornett*, S. I. El-Zanati, J. Jeffries**, and E. Rattin*, On 2-fold graceful graphs, submitted.
  34. H. Bermudez*, R. C. Bunge, E. D. Cornelius III*, S. I. El-Zanati, W. H. Mamboleo*, N. T. Nguyen*, and D. P. Roberts, The spectrum problem for two multigraphs with four vertices and seven edges, submitted.

Ongoing Projects:

  • C. Koskela*, M. Mattingly*, E. Pelttari**, and K. Shoukry, On cyclic (2Kmx+1,Cm)-designs.
  • M. Cornett* and E. Sparks*, On 2-fold graceful labelings of graphs.
  • J. Buchanan*, E. Pelttari*, G. Rasmuson**, A. Su****, and S. Tagaris*, On decompositions of complete multipartite graphs into the union of two cycles.
  • D. Gibson*, J. Nagel*, B. Stanley*, and A. Zale*, On cyclic decompositions of Kn+1,n+1-I into a 2-regular bipartite graph of size n.
  • N. Boone*, D. Collins**, M. Morris**, G. H. Seelinger****, and J. Utegaard*, On decompositions of circulant graphs into forests.
  • S. Allen**, K. Bosch*, L. Brown*, and R. Howard**, On (λKvKm,n)-designs.

Presentations

  1. J. A. Mudrock*, On decomposing complete graphs of odd order into Hamilton cycles and fixed length cycles, 2009 Joint Math Meetings, January 2009, Washington, DC.
  2. R. C. Bunge**, On gamma-labeling almost-bipartite 2-regular graphs, 2009 Joint Math Meetings, January 2009, Washington, DC.
  3. J. A. Mudrock*, On lambda-fold Rosa-type labelings, 2010 Joint Math Meetings, January 2010, San Francisco, CA.
  4. D. L. Masters**, On cyclic cycle plus a chord designs, 2010 Joint Math Meetings, January 2010, San Francisco, CA.
  5. R. C. Bunge**, On G-designs, where G is the one-point union of two cycles, 24th Midwestern Conference on Combinatorics, Cryptography, and Computing, September 2010, Normal, IL.
  6. R. C. Bunge**, On cyclic G-designs, 2011 Joint Math Meetings, January 2011, New Orleans, LA.
  7. C. K. Pawlak*, On G-designs, where G is the one-point union of two cycles, 2011 Joint Math Meetings, January 2011, New Orleans, LA.
  8. R. C. Bunge**, On Cyclic Decompositions of Complete Graphs into Tripartite Graphs, 42nd Southeastern International Conference on Combinatorics, Graph Theory, and Computing, March 2011, Boca Raton, FL.
  9. E. Sparks*, On 2-fold graceful labelings of graphs, 25th Midwestern Conference on Combinatorics, Cryptography, and Computing, October 2011, Las Vegas, NV.
  10. M. Cornett*, On 2-fold graceful labelings of graphs, 2012 AMS-MAA Joint Meetings, January 2012, Boston, MA.
  11. J. Buchanan*, E. Pelttari*, and S. Tagaris*, On d-modular labelings of the union of two cycles, 2012 AMS-MAA Joint Meetings, January 2012, Boston, MA.
  12. J. Klister* and C. Kruger*, On Rosa-type labelings of directed graphs, 2012 AMS-MAA Joint Meetings, January 2012, Boston, MA.
  13. S. Allen*, J. Bolt**, and S. Burton*, On 2-fold G-designs where G has order at most 4 and edge-multiplicity 2, 2012 AMS-MAA Joint Meetings, January 2012, Boston, MA.
  14. E. Sparks*, On 2-fold graceful labelings of graphs, The 2012 Annual Meeting of the Illinois Section of the MAA, March 2012, Normal, IL.
  15. J. Buchanan* and E. Pelttari*, On d-modular labelings of the union of two cycles, The 2012 Annual Meeting of the Illinois Section of the MAA, March 2012, Normal, IL.
  16. J. Klister* and C. Kruger*, On Rosa-type labelings of directed graphs, The 2012 Annual Meeting of the Illinois Section of the MAA, March 2012, Normal, IL.
  17. S. Allen*, On 2-fold G-designs where G has order at most 4 and edge-multiplicity 2, The 2012 Annual Meeting of the Illinois Section of the MAA, March 2012, Normal, IL.
  18. E. Sparks*, On 2-fold graceful labelings of graphs, MathFest 2012, August 2012, Madison WI.
  19. A. Hakes* and J. Torf*, On decomposing lambda-fold complete graphs into Stanton 4-cycles, 2013 AMS-MAA Joint Meetings, January 2013, San Diego, CA.
  20. D. Gibson*, B. Stanley*, and A. Zale*, On cyclic decompositions of Kn,n minus a 1-factor into 2-regular bipartite graphs, 2013 AMS-MAA Joint Meetings, January 2013, San Diego, CA.
  21. M. Ermete*, Tree decompositions of regular graphs and multigraphs, 2013 AMS-MAA Joint Meetings, January 2013, San Diego, CA.
  22. J. Nagel*, On cyclic decompositions of Kn,n minus a 1-factor into 2-regular bipartite graphs, 44th Southeastern Conference on Combinatorics, Graph Theory and Computing, March 2013, Boca Raton, FL.
  23. J. Jeffries* and E. Mastalio*, On decomposing lambda-fold complete graphs into Stanton 4-cycles, 44th Southeastern Conference on Combinatorics, Graph Theory and Computing, March 2013, Boca Raton, FL.
  24. E. K. Sparks**, On cyclic decompositions of Kn–1,n–1+I into a 2-regular bipartite graph of size n and at most 2 components, 2014 AMS-MAA Joint Meetings, January 2014, Baltimore, MD.
  25. A. Arias* and M. Carmona Herrera*, On cyclic decompositions of Kn–1,n–1+I into a 2-regular bipartite graph of size n and at most 2 components, 45th Southeastern Conference on Combinatorics, Graph Theory and Computing, March 2014, Boca Raton, FL.
  26. S. Allen*, On 2-fold G-designs where G has order at most 4 and edge-multiplicity 2, 45th Southeastern Conference on Combinatorics, Graph Theory and Computing, March 2014, Boca Raton, FL.
  27. N. Boone*, K. Kimball*, and M. Kopp*, On decomposing 2n-regular circulant graphs into forests with n edges, 45th Southeastern Conference on Combinatorics, Graph Theory and Computing, March 2014, Boca Raton, FL.
  28. H. Fry and N. Witt**, On the Spectrum Problem for Bipartite Digraphs of Small Order, 28th Midwestern Conference on Combinatorics, Cryptography, and Computing, October 2014, Las Vegas, Nevada.
  29. L. Cross**, E. Morales*, and K. Stilson*, On Cyclic and 1-Rotational G-Decompositions of 2-fold Complete Multigraphs, 28th Midwestern Conference on Combinatorics, Cryptography, and Computing, October 2014, Las Vegas, Nevada.
  30. S. Allen** and C. Shinners*, On λ-fold G-designs where G is a bipartite subgraph of 2K4, Forty-Sixth Southeastern International Conference on Combinatorics, Graph Theory, and Computing, March 2015, Boca Raton, Florida.
  31. E. Doebel*, P. Kilgus*, and S. Zeppetello**, On cyclic and 1-rotational multigraph designs, Forty-Sixth Southeastern International Conference on Combinatorics, Graph Theory, and Computing, March 2015, Boca Raton, Florida.
  32. K. Krauss*, C. Sullivan*, and A. Unsicker*, On the Spectrum Problem for Bipartite Digraphs of Small Order, Forty-Sixth Southeastern International Conference on Combinatorics, Graph Theory, and Computing, March 2015, Boca Raton, Florida.
  33. C. J. Cowan*, L. J. Cross**, A. E. Hart*, ​and A. M. Youngblood*, Decompositions of Complete Digraphs into Small Tripartite Digraphs, 29th Midwestern Conference on Combinatorics and Combinatorial Computing, Charleston, October 2015, Charleston, South Carolina.
  34. L. Febles Miranda*, J. P. Guadarrama*, E. Song**, and A. Zale**, Decompositions of Complete Multigraphs into Tripartite Multigraphs of Size 5, 29th Midwestern Conference on Combinatorics and Combinatorial Computing, October 2015, Charleston, South Carolina.
  35. C. Koskela*, M. Mattingly*, E. Pelttari**, and K. Shoukry*, On Cyclic Cm-decompositions of 2Kmx+1, 29th Midwestern Conference on Combinatorics and Combinatorial Computing, October 2015, Charleston, South Carolina.
  36. S. DeShong*, A. Fischer**, and L. Teng*, Decompositions of Complete Digraphs into Small Tripartite Digraphs, 30th Midwestern Conference on Combinatorics and Combinatorial Computing, October 2016, Normal, Illinois.
  37. B. Darrow*, T. Dubczuk*, H. Hao***, and G. Newkirk, Decompositions of Kn* into orientations of K4e, 30th Midwestern Conference on Combinatorics and Combinatorial Computing, October 2016, Normal, Illinois.
  38. J. Jeffries**, A. Sickman*, and K. Stilson**, The lambda-fold spectra for multigraphs of order 4 and size 6, 30th Midwestern Conference on Combinatorics and Combinatorial Computing, October 2016, Normal, Illinois.
  39. T. Dubczuk*, J. Kirkpatrick*, and A. Sickman*, The lambda-fold spectra of several multigraphs on 4 vertices with 6 edges and edge multiplicity at most 2, 48th Southeastern International Conference on Combinatorics, Graph Theory, & Computing, March 2017, Boca Raton, Florida.
  40. J. Jeffries**, On 2-fold graceful labelings of graphs, 48th Southeastern International Conference on Combinatorics, Graph Theory, & Computing, March 2017, Boca Raton, Florida.
  41. D. Gibson**, Decompositions of complete multigraphs into small tripartite multigraphs, 31st Midwestern Conference on Combinatorics and Combinatorial Computing, October 2017, Carrollton, Georgia.
  42. T. Dubczuk* and A. Sickman*, On the spectrum problem for digraphs of order 4 and size 6, 31st Midwestern Conference on Combinatorics and Combinatorial Computing, October 2017, Carrollton, Georgia.
  43. A. Cooper*, Decompositions of complete multigraphs into small tripartite multigraphs, 49th Southeastern International Conference on Combinatorics, Graph Theory, & Computing, March 2018, Boca Raton, Florida.
  44. J. Ward*, Spectrum problem for multigraph designs on four vertices and eight edges, 49th Southeastern International Conference on Combinatorics, Graph Theory, & Computing, March 2018, Boca Raton, Florida.
  45. J. Jetton** and A. Netz*, On the spectrum problem for the 3-uniform loose 5-cycle, 32nd Midwestern Conference on Combinatorics and Combinatorial Computing, October 2018, Duluth, Minnesota.
  46. M. Hamanaka*, C. Hatzer*, T. Mills*, and L. Nowak**, On the λ-fold spectrum problem for the connected cubic tripartite multigraphs of order 8, 32nd Midwestern Conference on Combinatorics and Combinatorial Computing, October 2018, Duluth, Minnesota.
  47. D. Collins**, D. Conko-Camel*, R. Liebrecht*, and A. Vasquez*, On maximum packings of λ-fold complete 3-uniform hypergraphs with loose 3-cycles, 32nd Midwestern Conference on Combinatorics and Combinatorial Computing, October 2018, Duluth, Minnesota.
  48. A. Armstrong**, W. Duncan*, K. Koe*, and R. Stutzman*, ​On the spectrum problem for the 3-uniform tri-star with 4 edges, 32nd Midwestern Conference on Combinatorics and Combinatorial Computing, October 2018, Duluth, Minnesota.

Poster Presentations

  • C. Benson**, K. Cronin*, and A. Paganin*, On Partitioning Zn into Arithmetic Progressions, Undergraduate Student Poster Session, 2009 Joint Math Meetings, Washington, DC.
  • L. Vickroy*, Coloring Graphs Properly with Edge-Weights, Undergraduate Student Poster Session, 2009 Joint Math Meetings, Washington, DC.
  • C. Witkowski***, Elementary Students and the Process of Generalization, Research Presession of the 2009 Annual Meeting and Exposition of the National Council of Teachers of Mathematics, Washington, DC.
  • D. I. Gannon*, On labelings of some cycle-based graphs, Undergraduate Student Poster Session, 2010 Joint Math Meetings, San Francisco, CA.
  • L. G. Allen**, R. C. Bunge**, D. I. Gannon*, K. A. Knee*, J. A. Mudrock*, and J. L. Smith*, On 2-fold G-designs where G is a cycle with a double-edge, Undergraduate Student Poster Session, 2010 Joint Math Meetings, San Francisco, CA.
  • I. Almeida-Arrieta**, R. C. Bunge**, T. A. Kamykowski, and D. L. Masters, On 2-fold gamma-labelings of odd cycles plus a chord, Undergraduate Student Poster Session, 2010 Joint Math Meetings, San Francisco, CA.
  • T. Bristol*, M. VanDuyne*, and K. Weigandt**, Elementary Students' Use of Representation in Developing Generalizations, 2010 Joint Math Meetings, San Francisco, CA.
  • D. Collins* and V. Morgan*, On nearly graceful labelings of 2-regular graphs, Undergraduate Student Poster Session, 2010 Joint Math Meetings, San Francisco, CA.
  • S. D. DeShong* and L. F. Teng*, Decompositions of complete digraphs into small tripartite digraphs, Young Mathematicians Conference 2016, Ohio State University, Columbus, OH.

Sample Topics Modules

Additional Evaluation & Support Materials

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