Tight paths in convex geometric hypergraphs
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, Sutherland, Kupitz and Perles for convex geometric graphs, as well as the classical Erdős-Gallai Theorem for graphs. As a consequence, we obtain the first substantial improvement on the Turán problem for tight paths in uniform hypergraphs.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2017
- DOI:
- 10.48550/arXiv.1709.01173
- arXiv:
- arXiv:1709.01173
- Bibcode:
- 2017arXiv170901173F
- Keywords:
-
- Mathematics - Combinatorics;
- 05C
- E-Print:
- Present version: 12 pages, 3 figures. We improve results and presentation of an earlier version, and removed results on crossing paths and matchings which will appear in a forthcoming paper