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Obligatory hypergraphs

Christian Reiher

Abstract

Erdős and Hajnal proved that every graph of uncountable chromatic number contains arbitrarily large finite, complete, bipartite graphs. We extend this result to hypergraphs.

Obligatory hypergraphs

Abstract

Erdős and Hajnal proved that every graph of uncountable chromatic number contains arbitrarily large finite, complete, bipartite graphs. We extend this result to hypergraphs.
Paper Structure (2 sections, 3 theorems, 4 equations, 2 figures)

This paper contains 2 sections, 3 theorems, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The proof

Key Result

Theorem 1.1

A finite graph is obligatory if and only if it is bipartite. ∎

Figures (2)

  • Figure 1.1: Some expansions
  • Figure 2.1: A delta system with root $\{\beta, \upsilon\}$

Theorems & Definitions (8)

  • Theorem 1.1: Erdős and Hajnal
  • Theorem 1.2
  • Corollary 2.2
  • proof : Proof of Theorem \ref{['thm:12']}
  • Claim 2.3
  • proof
  • Claim 2.4
  • proof