Tight paths in convex geometric hypergraphs

@article{Furedi2020TightPI,
  title={Tight paths in convex geometric hypergraphs},
  author={Zolt'an Furedi and Tao Jiang and Alexandr V. Kostochka and Dhruv Mubayi and Jacques Verstraete},
  journal={Advances in Combinatorics},
  year={2020}
}
One of the most intruguing conjectures in extremal graph theory is the conjecture of Erdős and Sós from 1962, which asserts that every $n$-vertex graph with more than $\frac{k-1}{2}n$ edges contains any $k$-edge tree as a subgraph. Kalai proposed a generalization of this conjecture to hypergraphs. To explain the generalization, we need to define the concept of a tight tree in an $r$-uniform hypergraph, i.e., a hypergraph where each edge contains $r$ vertices. A tight tree is an $r$-uniform… 

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