- Series
- Combinatorics Seminar
- Time
- Friday, February 27, 2026 - 3:15pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Jonathan Tidor – Princeton University – jtidor@princeton.edu – https://web.math.princeton.edu/~jt4085/
- Organizer
- Jiaxi Nie
The degeneracy of a graph is a measure of sparseness that appears in many contexts throughout graph theory. In extremal graph theory, it is known that graphs of bounded degeneracy have Ramsey number which is linear in their number of vertices (Lee, 2017). Also, the degeneracy gives good bounds on the Turán exponent of bipartite graphs (Alon--Krivelevich--Sudokav, 2003). Extending these results to hypergraphs presents a challenge, as it is known that the naïve generalization of these results -- using the standard notion of hypergraph degeneracy -- are not true (Kostochka--Rödl 2006). We define a new measure of sparseness for hypergraphs called skeletal degeneracy and show that it gives information on both the Ramsey- and Turán-type properties of hypergraphs.
Based on joint work with Jacob Fox, Maya Sankar, Michael Simkin, and Yunkun Zhou