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Seminar Details

Hypercube Turán Problems

  • Start Date: December 1, 2025
  • Event Start Time: 2:00 PM
  • Event End Time: 3:00 PM
  • Seminar Series: Rutgers Discrete Mathematics Seminar
  • Presenter(s): Daniel Zhu - Princeton University
  • Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
  • Presentation Type: Stand Alone Presentation
  • Abstract:

    What is the smallest subset of the hypercube {0, 1}^n that intersects every two-dimensional face? What is the largest subgraph of the hypercube graph Q_n that doesn't contain an 8-cycle? These questions are all examples of Turán problems on the hypercube, where we seek the minimum size of a subset (of either vertices and edges) of the hypercube that guarantees the existence of a certain structure. We discuss a framework for tackling such questions and some unexpected connections to structural graph theory and matroids.