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Tight paths in convex geometric hypergraphs
- Publication Year :
- 2020
-
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.<br />Comment: 14 pages, 3 figures
- Subjects :
- Mathematics - Combinatorics
05C
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2002.09457
- Document Type :
- Working Paper