IB-homogeneous graphs
arXiv:1909.02920
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.
19 pages, 2 figures. The new version includes a correct proof of Proposition 22 (Lemma 21 in the first version)