Tight paths in convex geometric hypergraphs
Combinatorics
2020-03-30 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 [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.
Keywords
Cite
@article{arxiv.2002.09457,
title = {Tight paths in convex geometric hypergraphs},
author = {Zoltán F\" uredi and Tao Jiang and Alexandr Kostochka and Dhruv Mubayi and Jacques Verstraëte},
journal= {arXiv preprint arXiv:2002.09457},
year = {2020}
}
Comments
14 pages, 3 figures