1. Tight paths in convex geometric hypergraphs
- Author
-
uredi, Zoltán F\", Jiang, Tao, Kostochka, Alexandr, Mubayi, Dhruv, and Verstraëte, Jacques
- Subjects
Mathematics - Combinatorics ,05C - Abstract
In this paper, we prove a theorem on tight paths in convex geometric hypergraphs, which is asymptotically sharp in infinitely many cases. Our geometric theorem is a common generalization of early results of Hopf and Pannwitz [12], Sutherland [19], Kupitz and Perles [16] for convex geometric graphs, as well as the classical Erd\H{o}s-Gallai Theorem [6] for graphs. As a consequence, we obtain the first substantial improvement on the Tur\'an problem for tight paths in uniform hypergraphs., Comment: 14 pages, 3 figures
- Published
- 2020