Tight paths in convex geometric hypergraphs
Combinatorics
2024-08-21 v2
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 Erd\H{o}s-Gallai Theorem for graphs. As a consequence, we obtain the first substantial improvement on the Tur\'{a}n problem for tight paths in uniform hypergraphs.
Keywords
Cite
@article{arxiv.1709.01173,
title = {Tight paths in convex geometric hypergraphs},
author = {Zoltán Füredi and Tao Jiang and Alexandr Kostochka and Dhruv Mubayi and Jacques Verstraëte},
journal= {arXiv preprint arXiv:1709.01173},
year = {2024}
}
Comments
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