Grace McCourt (UIUC)
A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs
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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.
