IB-homogeneous graphs

TL;DR

This paper classifies IB-homogeneous graphs, showing they are either ultrahomogeneous or MB-homogeneous, extending previous classifications and completing the understanding of these graph types up to bimorphism-equivalence.

Contribution

It extends existing classifications by proving IB-homogeneous graphs are either ultrahomogeneous or MB-homogeneous, completing their classification up to bimorphism-equivalence.

Findings

IB-homogeneous graphs are either ultrahomogeneous or MB-homogeneous

All IB-homogeneous graphs are classified up to bimorphism-equivalence

The classification extends the Lachlan-Woodrow Theorem and previous work on MB-homogeneous graphs

Abstract

The Lachlan-Woodrow Theorem identifies ultrahomogeneous graphs up to isomorphism. Recently, the present author and D. Hartman classified MB-homogeneous graphs up to bimorphism-equivalence. We extend those results in this paper, showing that every IB-homogeneous graph is either ultrahomogeneous or MB-homogeneous, and thus all the IB-homogeneous graphs are known up to bimorphism-equivalence.