Bob Krueger

Carnegie Mellon University, Department of Mathematical Sciences
Contact: rkrueger at andrew.cmu.edu
Office: Wean Hall 7216

I started an NSF postdoc at Carnegie Mellon University in Fall 2024, sponsored by Prasad Tetali. For the Spring 2025 semester, I will be a postdoc at the Simons Laufer Math Institute (formerly MSRI). I finished my math Ph.D. at the University of Illinois, Urbana-Champaign in Summer 2024, advised by József Balogh, where I held an NSF Graduate Research Fellowship. I earned undergraduate degrees at Miami University, where I majored in math and physics, and minored in statistics and computer science, and I was mentored by Louis DeBiasio.

My research interests generally lie in extremal and probabilistic combinatorics. I enjoy teaching at all levels and mentoring undergraduate research. At UIUC, I helped organize the Combinatorics Literature Seminar at UIUC, the Graph Theory and Combinatorics Seminar at UIUC, and CMPS, a two-time virtual meeting between UIUC, Iowa State, and University of Montana.

Papers

  1. Clique covers and decompositions of cliques of graphs [arXiv] [Submitted],
    with József Balogh, Jialin He, The Nguyen, Michael C. Wigal.
  2. Rational exponents for cliques [arXiv] [Submitted],
    with Sean English, Anastasia Halfpap.
  3. Lipschitz functions on weak expanders [arXiv] [Submitted],
    with Lina Li, Jinyoung Park.
  4. Triangle Percolation on the Grid [arXiv] [Discrete & Computational Geometry, 2024],
    with Igor Araujo, Bryce Frederickson, Bernard Lidický, Tyrrell B. McAllister, Florian Pfender, Sam Spiro, Eric Nathan Stucky.
    Started at GRWC.
  5. Realizable Standard Young Tableaux [arXiv] [Submitted],
    with Igor Araujo, Alexander E. Black, Amanda Burcroff, Yibo Gao, Alex McDonough.
    Started at GRWC.
  6. On oriented cycles in randomly perturbed digraphs [arXiv] [Combinatorics, Probability & Computing, 2023],
    with Igor Araujo, József Balogh, Simón Piga, Andrew Treglown.
  7. A sharp threshold for a random version of Sperner's Theorem [arXiv] [Random Structures & Algorithms, 2024],
    with József Balogh.
  8. Sharp threshold for the Erdős-Ko-Rado theorem [arXiv] [Random Structures & Algorithms, 2023],
    with József Balogh, Haoran Luo.
  9. Lower bounds on the Erdős-Gyárfás problem via color energy graphs [arXiv] [Journal of Graph Theory, 2023],
    with József Balogh, Sean English, Emily Heath.
  10. A note about monochromatic components in graphs of large minimum degree [arXiv] [Discussiones Mathematicae Graph Theory, 2021],
    with Louis DeBiasio.
  11. Generalized Ramsey numbers: forbidding paths with few colors [arXiv] [Electronic Journal of Combinatorics, 2020].
    Product of CUNY's combinatorics REU.
  12. Partitioning the power set of [n] into C_k-free parts [arXiv] [Electronic Journal of Combinatorics, 2019],
    with Eben Blaisdell, András Gyárfás, Ronen Wdowinski.
    Completed during my 'Budapest' semester.
  13. Long monochromatic paths and cycles in 2-colored bipartite graphs [arXiv] [Discrete Mathematics, 2020],
    with Louis DeBiasio.
  14. Large monochromatic components in multicolored bipartite graphs [arXiv] [Journal of Graph Theory, 2019],
    with Louis DeBiasio, Gábor N. Sárközy.
  15. Monochromatic balanced components, matchings, and paths in multicolored complete bipartite graphs [arXiv] [Journal of Combinatorics, 2020],
    with Louis DeBiasio, András Gyárfás, Miklós Ruszinkó, Gábor N. Sárközy.
  16. Hamiltonian cycles in k-partite graphs [arXiv] [Journal of Graph Theory, 2019],
    with Louis DeBiasio, Dan Pritikin, Eli Thompson.
    My first project, done at Miami.

Advising

  1. List coloring with requests for planar graphs [Report] [Poster].
    Project done by undergraduates I advised with Peter Bradshaw at the IML in Fall 2023.
  2. Polymath Jr. Distinct Distances [Presentation].
    Project done online by a large group of undergraduates I helped mentor in Summer 2023.
  3. Manipulation in voting theory [Report] [Presentation].
    Project done by local high school students I advised at the IML in Summer 2022.
  4. Edge-colorings without small substructures [Report] [Poster].
    Project done by undergraduates I advised with Sean English at the IML in Spring 2022.
  5. Investigations in combinatorial game theory [Report] [Presentation].
    Project done by local high school students I advised at the IML in Summer 2020.
  6. Firefighting on the Hexagonal Grid and on Infinite Trees [arXiv] [Discrete Applied Mathematics, 2021].
    Written by undergraduates I advised with Sean English at the IML in Spring 2020.

Teaching

  1. Fall 2020: Recitation for Calculus I at UIUC.
    Ranked outstanding by my students.
    This was a Merit section: a (non-remedial) program
    which offers more student interaction and instructor independence for disadvantaged students.
  2. Spring 2020: Recitation for Calculus II at UIUC.
    Ranked excellent by my students.
  3. Fall 2019: Recitation for Calculus I at UIUC.
    Ranked excellent by my students.
  4. Undergraduate Supplemental Instructor at Miami for
    Differential Equations for Engineers, Calculus I, Linear Algebra.
    Included educational training.

Games