# The independence number of HH-homogeneous graphs and a classification of MB-homogeneous graphs

## TL;DR

This paper investigates the properties of certain infinite graphs, establishing bounds on their independence number and classifying MB-homogeneous graphs based on their structural equivalences.

## Contribution

It proves the finiteness of the independence number for specific HH-homogeneous graphs and provides a classification of MB-homogeneous graphs up to bimorphism-equivalence.

## Key findings

- Independence number of HH-homogeneous graphs without Rado graph is finite
- Classification of MB-homogeneous graphs up to bimorphism-equivalence
- Structural insights into infinite homogeneous graphs

## Abstract

We show that the independence number of a countably infinite HH-homogeneous graph that does not contain the Rado graph as a spanning subgraph is finite and present a classification of MB-homogeneous graphs up to bimorphism-equivalence as a consequence.