Trees and $n$-Good Hypergraphs

Abstract

Trees fill many extremal roles in graph theory, being minimally connected and serving a critical role in the definition of $n$-good graphs. In this article, we consider the generalization of trees to the setting of $r$-uniform hypergraphs and how one may extend the notion of $n$-good graphs to this setting. We prove numerous bounds for $r$-uniform hypergraph Ramsey numbers involving trees and complete hypergraphs and show that in the $3$-uniform case, all trees are $n$-good when $n$ is odd or $n$ falls into specified even cases.

23 pages, 3 figures, 2 tables

Cited by in corpus (2)

• Constructive Methods in Gallai-Ramsey Theory for Hypergraphs
• Minimally Connected Hypergraphs