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, sponsered by Prasad Tetali. 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. 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. Lipschitz functions on weak expanders [arXiv],
    with Lina Li, Jinyoung Park
  2. Triangle Percolation on the Grid [arXiv] [Discrete & Computational Geometry],
    with Igor Araujo, Bryce Frederickson, Bernard Lidický, Tyrrell B. McAllister, Florian Pfender, Sam Spiro, Eric Nathan Stucky.
    Started at GRWC.
  3. Realizable Standard Young Tableaux [arXiv],
    with Igor Araujo, Alexander E. Black, Amanda Burcroff, Yibo Gao, Alex McDonough.
    Started at GRWC.
  4. On oriented cycles in randomly perturbed digraphs [arXiv] [Combinatorics, Probability & Computing],
    with Igor Araujo, József Balogh, Simón Piga, Andrew Treglown.
  5. A sharp threshold for a random version of Sperner's Theorem [arXiv] [Accepted to Random Structures & Algorithms],
    with József Balogh.
  6. Sharp threshold for the Erdős-Ko-Rado theorem [arXiv] [Random Structures & Algorithms, 2023],
    with József Balogh, Haoran Luo.
  7. Lower bounds on the Erdős-Gyárfás problem via color energy graphs [arXiv] [Journal of Graph Theory, 2023],
    with József Balogh, Sean English, Emily Heath.
  8. A note about monochromatic components in graphs of large minimum degree [arXiv] [DMGT, 2021],
    with Louis DeBiasio.
  9. Generalized Ramsey numbers: forbidding paths with few colors [arXiv] [Electronic Journal of Combinatorics, 2020].
    Product of CUNY's combinatorics REU.
  10. 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.
  11. Long monochromatic paths and cycles in 2-colored bipartite graphs [arXiv] [Discrete Mathematics, 2020],
    with Louis DeBiasio.
  12. Large monochromatic components in multicolored bipartite graphs [arXiv] [Journal of Graph Theory, 2019],
    with Louis DeBiasio, Gábor N. Sárközy.
  13. 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.
  14. 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 and Teaching

  1. List coloring with requests for planar graphs
    Project done by undergraduates I advised at the IGL in Fall 2023.
  2. Manipulation in voting theory [IGL wiki].
    Project done by local high school students I advised at the IGL in Summer 2022.
  3. Edge-colorings without small substructures [IGL wiki].
    Project done by undergraduates I advised at the IGL in Spring 2022.
  4. Investigations in combinatorial game theory [IGL wiki].
    Project done by local high school students I advised at the IGL in Summer 2020.
  5. Firefighting on the Hexagonal Grid and on Infinite Trees [arXiv] [Discrete Applied Mathematics, 2021].
    Written by undergraduates I advised at the IGL in Spring 2020. See the IGL wiki for a poster and presentation.
  6. Recitation Sections at UIUC: Calculus I (Fall 2019, Fall 2020), Calculus II (Spring 2020).
    Ranked outstanding by my students in Fall 2020.

Games