Tight paths in convex geometric hypergraphs

Zoltán Füredi, Tao Jiang, Alexandr Kostochka, Dhruv Mubayi, Jacques Verstraëte

Research output: Contribution to journalArticle

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 Erdős-Gallai Theorem [6] for graphs. As a consequence, we obtain the first substantial improvement on the Turán problem for tight paths in uniform hypergraphs.

Original languageEnglish (US)
Article number1
Pages (from-to)1-14
Number of pages14
JournalAdvances in Combinatorics
Volume2020
Issue number1
DOIs
StatePublished - 2020

Keywords

  • Convex geometric hypergraphs
  • Paths
  • Turan number

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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