Linear trees in uniform hypergraphs

TL;DR

This paper investigates the Turan number of k-expansions of trees in uniform hypergraphs, providing asymptotic results using the delta-system method to determine the maximum size of T^k-free hypergraphs.

Contribution

It introduces a method to asymptotically determine the Turan number for k-expansions of trees in hypergraphs, expanding understanding of hypergraph extremal problems.

Findings

Asymptotic Turan number for T^k in n-vertex hypergraphs

Application of delta-system method to hypergraph extremal problems

Characterization of largest T^k-free hypergraphs

Abstract

Given a tree T on v vertices and an integer k exceeding one. One can define the k-expansion T^k as a k-uniform linear hypergraph by enlarging each edge with a new, distinct set of (k-2) vertices. Then T^k has v+ (v-1)(k-2) vertices. The aim of this paper is to show that using the delta-system method one can easily determine asymptotically the size of the largest T^k-free n-vertex hypergraph, i.e., the Turan number of T^k.