Homogeneous digraphs

Descendant-homogeneous digraphs

The descendant set desc(α) of a vertex α in a digraph D is the set of vertices which can be reached by a directed path from α. A subdigraph of D is finitely generated if it is the union of finitely many descendant sets and D is descendant-homogeneous if it is vertex transitive and any isomorphism between finitely generated subdigraphs extends to an automorphism. We consider connected descendant...

Homogeneous 2-partite digraphs

We call a 2-partite digraph D homogeneous if every isomorphism between finite induced subdigraphs that respects the 2-partition of D extends to an automorphism of D that does the same. In this note, we classify the homogeneous 2-partite digraphs.

Locally-finite connected-homogeneous digraphs

Classification of some countable descendant-homogeneous digraphs

For finite q, we classify the countable, descendant-homogeneous digraphs in which the descendant set of any vertex is a q-valent tree. We also give conditions on a rooted digraph Γ which allow us to construct a countable descendant-homogeneous digraph in which the descendant set of any vertex is isomorphic to Γ. 2010 Mathematics Subject Classification: 05C20, 05C38, 20B27

Homogeneous factorisations of graphs and digraphs

A homogeneous factorisation (M,G,Γ,P) is a partition P of the arc set of a digraph Γ such that there exist vertex transitive groups M < G 6 Aut(Γ) such that M fixes each part of P setwise while G acts transitively on P. Homogeneous factorisations of complete graphs have previously been studied by the second and fourth authors, and are a generalisation of vertex-transitive self-complementary dig...