Complete r-partite subgraphs of dense r-graphs

TL;DR

This paper investigates the maximum size of r-partite subgraphs within dense r-uniform graphs, refining Erdős's 1964 results by establishing bounds based on the number of vertices and edges.

Contribution

It provides a more precise characterization of r-partite subgraphs in dense r-graphs, improving upon classical bounds from Erdős's work.

Findings

Determines the maximum size of r-partite subgraphs in dense r-graphs.

Refines Erdős's 1964 results with tighter bounds.

Establishes that the size depends on a slowly decreasing function of n.

Abstract

We determine how large r-partite graphs can be found in r-uniform graphs with n vertices and Cn^r edges, where C is a slowly decreasing function of n. This refines results of Erdos from 1964.