Seminar Details
A Hypergraph Analog of Dirac's Theorem for Long Cycles in 2-connected Graphs
- Start Date: April 19, 2023
- Event Start Time: 12:15 PM
- Event End Time: 1:15 PM
- Seminar Series: Graduate Combinatorics Seminar
- Presenter(s): Grace McCourt - University of Illinois, Urbana-Champaign
- Event Location: Online Event
- Event Additional Info: <p>Presented on zoom: <a href="https://rutgers.zoom.us/j/93717937010?pwd=Z2RyY01HKzVhVFlXRXR1anluRFIvQT09">https://rutgers.zoom.us/j/93717937010?pwd=Z2RyY01HKzVhVFlXRXR1anluRFIvQT09</a></p> <p>      Meeting ID: 937 1793 7010</p> <p>      Password: gcs2023</p> <p>See: <a href="https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html">https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html</a></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
Dirac proved that each n-vertex 2-connected graph with minimum degree at least k contains a cycle of length at least min{2k, n}. We prove a hypergraph version of this result: for n geq k geq r+2 geq 5, every 2-connected r-uniform n-vertex hypergraph with minimum degree at least {k-1 choose r-1}+1 has a Berge cycle of length at least min{2k, n}. The bound is exact for all k geq r+2 geq 5. This work is joint with Alexandr Kostochka and Ruth Luo.