I am a professor at Iowa State University and Editor-in-Chief of the journal Order, published by Springer.

My fields of interest are extremal poset theory, graph theory and extremal and probabilistic combinatorics. CV, Publications

I was a Fulbright US Scholar as part of the Budapest Semesters in Mathematics program at the Alfred Rényi Institute of Mathematics in 2019. I was also a visitor of Maria Axenovich at the Karlsruhe Institute of Technology, Germany via the German Academic Exchange Service (DAAD) in 2020.

• The discrete mathematics research cluster is partially supported by Research Training Grant (RTG) #1839918 from the National Science Foundation (NSF).
• My research is partially supported by a grant from the Simons Foundation (#353292, 2015-2020) (#709641, 2020-2025)

• Graph clustering via generalized colorings, with A. London and A. Pluhár, submitted.
• Counting paths, cycles and blow-ups in planar graphs, with C. Cox, submitted.
• On the edit distance function of the random graph, with A.W.N. Riasanovsky, submitted.
• Splits with forbidden subgraphs, with M. Axenovich, submitted.
• Planar Turán number of the 6-cycle, with D. Ghosh, E. Gyõri, A. Paulos, and C. Xiao, submitted.
• The maximum number of paths of length four in a planar graph, with D. Ghosh, E. Gyõri, A. Paulos, N. Salia, C. Xiao, and O. Zamora, Discrete Math., to appear.
• Induced and non-induced poset saturation problems, with B. Keszegh, N. Lemons, D. Pálvölgyi, B. Patkós, J. Combin. Theory Ser. A, to appear.
• Counterexamples to a conjecture of Harris on Hall Ratio, with A. Blumenthal, B. Lidický, S. Norin, F. Pfender, and J. Volec, SIAM J. Discrete Math., to appear.

• Improved bounds for induced poset saturation, with H.C. Smith and S. Walker, Electron. J. Combin., 27(2) (2020), Research Paper P2.31. (9pp.) [Journal Link]
• On difference graphs and the local dimension of posets, with J. Kim, T. Masařík, W. Shull, H.C. Smith, A. Uzzell, and Z. Wang, European J. Combin., 86 (2020), Article 103074. [Journal Link]
• Ore and Chvátal-type degree conditions for bootstrap percolation from small sets, with M. Dairyko, M. Ferrara, B. Lidický, F. Pfender, and A. Uzzell, J. Graph Theory, 94(2) (2020), 252--266. [Journal Link]
• Regular colorings and factors of regular graphs, with A. Bernshteyn, O. Khormali, J. Rollin, D. Rorabaugh, S. Shan, and A. Uzzell, Discuss. Math. Graph Theory, 40(3) (2020), 795--806. [Journal Link]
• A simple proof for a forbidden subposet problem, with A. Methuku, A. Uzzell, and S. Walker, Electron. J. Combin., 27(1) (2020), Research Paper P1.31. (9pp.) [Journal Link]

• MATH 314: Graph Theory
  • Textbook: G. Chartrand and P. Zhang, A First Course in Graph Theory, Dover books on mathematics, 2012, 450pp.
  • Canvas:  https://canvas.iastate.edu
  • WebEx room: https://iastate.webex.com/meet/rymartin

• Edit distance survey: The edit distance in graphs: methods, results and generalizations, Recent Trends in Combinatorics, 31--62, IMA Vol. Math. Appl., 159, Springer, Cham, 2016. [Errata]
• Lake Michigan Workshop slides: "The edit distance on graphs": Part I, Part II, Part III
• Current and former students.
• Discrete Math seminar page (maintained by Bernard Lidický).