Combinatorics, Graph Theory, and More

Some of my papers are available at the Mathematics ArXiv, or MathSciNet.


Papers & Other Writing

  • N. Bushaw, P. Csorba, L. Erickson, D. Gerbner, D. Piguet, A. Riet, T. Terpai, D.K. Vu."Large Matchings with Few Colors". Technical Report. [arXiv:1209.2033]
  • N. Bushaw, N. Kettle. "Turan numbers of Multiple Paths and Equibipartite Trees." Combinatorics, Probability and Computing, 20 (2011) pp 837-853. [arXiv:1106.5904]
  • N. Bushaw. "Problems in Extremal Combinatorics." PhD Dissertation. Major Professor: Dr. Bela Bollobas, University of Memphis. May 2012. [pdf]
  • N. Bushaw, N. Kettle. "Turan numbers for Forests of Paths in Hypergraphs". SIAM J. Discrete Math., 28-2 (2014) pp 711-721. [arXiv:1303.5022]
  • N. Bushaw, M. Collares Neto, R. Morris, P. Smith. "The sharp threshold for maximum-size sum-free subsets in even-order abelian groups". Combinatorics, Probability, and Computing 20, no. 4 (2015) pp 609-640. [arXiv:1310.3236]
  • N. Bushaw, K. Gunderson, S. Kalikow. "Random-step Markov Processes". Israel Journal of Mathematics 216 (1) (2016) pp 181-214. [arXiv:1410.1457]
  • J. Balogh, N. Bushaw, M. Collares Neto, H. Liu, R. Morris, M. Sharifzadeh. "The Typical Structure of Graphs with No Large Cliques". Combinatorica 37 (4) (2017) pp 617-632.[arXiv:1406.6961]
  • N. Bushaw, N. Kettle. "Threshold Pebbling for Grids". Submitted.
  • N. Bushaw, N. Kettle. "Turan numbers for Forestable Graphs". Submitted.
  • N. Bushaw, C. Larson, N. Van Cleemput, and Summer 2017 Graph Brain Project Workshop Participants. "Automated Conjecturing VII: The Graph Brain Project and Big Mathematics". Submitted. [arXiv:1801.01814]
  • N. Bushaw, D. Cranston. "A Note on Bootstrap Percolation Thresholds in Plane Tilings using Regular Polygons". Submitted. [arXiv:1803.09056]
  • N. Bushaw, A. Czygrinow, J. Yie. "Even Cycles in Dense Graphs". In progress.

Upcoming Talks:

  • 6 June 2018. "Thresholds for Random Pebbling", SIAM Discrete Math, University of Colorado at Denver, Denver, CO, USA.
  • July 2018. "The Even Cycle Spectrum of Dense Graphs", 10th International Colloquium on Graph Theory and Combinatorics, University Lyon 1, La Doua, Lyon, France.

Past Research Talks:

  • Apr 2018. "Bootstrap Percolation on Polygonal Tilings", MAA Sectional Meeting, Virginia Military Institute, Lexington, VA, USA>.
  • Mar 2018, "Automated Conjecturing and Collaborative Mathematics", Forty-Ninth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA.
  • Jan 2018, "2-Connected Graphs Have Many Cycle Lengths", Discrete Math Seminar, Virginia Commonwealth University, Richmond, VA, USA.
  • Sep 2017, "TurĂ¡n Numbers and their Variants", Discrete Math Seminar, Virginia Commonwealth University, Richmond, VA, USA.
  • Apr 2017, "The Even Cycle Spectrum of Dense Graphs", AMS Special Session on Extremal Problems in Graphs, Hypergraphs and Other Combinatorial Structures, Spring Central Sectional Meeting, Indiana University, Bloomington, IN, USA.
  • Jan 2017, "Variations on a Theme: The Forbidden Subgraph Problem", Mathematics Colloquium, Virginia Commonwealth University, Richmond, VA, USA.
  • Apr 2016, "Minimum Codegree Conditions for Tiling by Tight Cycles", AMS Special Session on Probabilistic and Extremal Combinatorics, AMS Spring North Sectional Meeting, North Dakota State University, Fargo, ND, USA. (Invited)
  • Jan 2016, "Extremal Numbers for Forestable Graphs", AMS-MAA Joint Meetings, Seattle, WA, USA.
  • Nov 2015, "The Forbidden Subgraph Problem and its Variants", Postdoc Lunch Seminar Series, Arizona State University, Tempe, AZ, USA.
  • Oct 2015, "Threshold Pebbling on Grids of Arbitrary Dimension", AMS Special Session on Probabilistic Combinatorics, AMS Fall Southeastern Sectional Meeting, University of Memphis, Memphis, TN, USA. (Invited)
  • Sep 2015, "Pebbling Problems on Graphs", Discrete Math Seminar, Arizona State University, Tempe, AZ.
  • Jun 2015, "Threshold Pebbling for Grids", Connections in Discrete Mathematics, Simon Fraser University, Burnaby, BC, CA.
  • Mar 2015, "Introduction to Hypergraph Containers", Discrete Math Seminar, Arizona State University, Tempe, AZ, USA.
  • Jan 2015, "Supersaturation Theorems, Hypergraph Containers, and Typical Structures", Discrete Math Seminar, Arizona State University, Tempe, AZ, USA.
  • Oct 2014, "Typical Structure of Graphs with No Large Clique", Postdoc Lunch Seminar Series, Arizona State University, Tempe, AZ, USA.
  • Jan 2014, "Random Markov Processes", Mathematics and Computer Science Seminar, Universidade Federal do Ceara, Fortaleza, Brazil.
  • Nov 2013, "Random Markov Processes", Probability Seminar, Arizona State University, Tempe, AZ, USA.
  • Oct 2013, "The Sharp Threshold for Maximum-Size Sum-Free Subsets in Even-Order Abelian Groups", Discrete Math Seminar, Arizona State University, Tempe, AZ, USA.
  • Sep 2013, "Turan Numbers of Linear and Equibipartite Forests", Discrete Math Seminar, Arizona State University, Tempe, AZ, USA.
  • Dec 2012, "Turan numbers of Equibipartite Forests and Forests of Hyperpaths", Theoretical Computer Science and Combinatorics Seminar, Universidade do Sao Paulo, Sao Paulo, Brazil.
  • Dec 2012, "Turan numbers of Linear and Equibipartite Forests", Mathematics and Computer Science Seminar, Universidade Federal do Ceara, Fortaleza, Brazil.
  • Nov 2011, "Turan Numbers for Multiple Paths", Atlanta Lecture Series in Combinatorics and Graph Theory IV, Georgia State University, Atlanta, GA, USA.
  • Oct 2011, "Turan Numbers for Multiple Paths and Some Forests", Discrete Mathematics Seminar, University of Nebraska, Lincoln, NE, USA.
  • Aug 2011, "Turan Numbers for Multiple Paths and Equibipartite Trees", Paul Turan Memorial Conference, Renyi Institute of Mathematics, Budapest, Hungary.
  • Apr 2011, "Turan Numbers for Multiple Paths and Equibipartite Trees", Combinatorics Seminar, University of Memphis, Memphis, TN, USA.
  • May 2008, "Ramsey Theory and Applications", Mathematics Colloquium, Western Washington University, Bellingham, WA, USA.

Past Outreach Talks:

  • May 2018, "Percolation Among Zombies", VCU Math Circle, Virginia Commonwealth University, Richmond, VA. (Audience: High School Students)
  • Apr 2018, "Bootstrap Percolation", Society of Physics Students, Virginia Commonwealth University, Richmond, VA. (Audience: Physics majors and graduate students)
  • Dec 2017, "Conway's Rational Tangles", Sonya Kovalevsky Girls In Math Day, Virginia Commonwealth University, Richmond, VA. (Audience: Junior High / Middle School Students)
  • Apr 2016, "Mad Scientists, Permutations, and Combinatorics", ASU Math Circle, Arizona State University, Tempe, AZ. (Audience: High School Students)
  • Apr 2016, "Conway's Rational Tangles", Mathematics Awareness Day Workshop, Arizona State University, Tempe, AZ, USA. (Audience: High School Students)
  • Sep 2015, "Winning Strategies", ASU Math Circle, Arizona State University, Tempe, AZ. (Audience: High School Students)
  • Sep 2015, "Intro to Extremal Graph Theory", ASU Math Club, Arizona State University, Tempe, AZ. (Audience: Undergraduate Mathematics Majors)
  • 3
  • Apr 2015, "The Mathematics of Billiards and Reflections", Mathematics Awareness Day Workshop, Arizona State University, Tempe, AZ, USA. (Audience: High School Students. Joint w/ T. Stepien, M. Kawski)
  • Nov 2011, "Voting Theory: Why it isn't fair", Cantor Sect Undergraduate Mathematics Club, University of Memphis, Memphis, TN, USA.