Homogeneous 2-partite digraphs

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.

Cyclically k-partite digraphs and k-kernels

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent set of vertices (if u, v ∈ N then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l). A k-kernel is a (k, k − 1)-kernel. A digraph D is cyclically k-partite if there exists a partition {Vi} i=0 of V (D) suc...

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...

Locally-finite connected-homogeneous digraphs

Evenly partite bigraph-factorization of symmetric complete tripartite digraphs

We show that a necessary and sufficient condition for the existence of a Kp ,2q factorization of the symmetric complete tripartite digraph K~1,n2,n3 is (i) ni = n2 = n3 == 0 (mod p) for p = q, (ii) ni = n2 = n3 == 0 (mod dp'q'(p' + 2q')) for p =Iq and p' odd, (iii) ni = n2 = n3 == 0 (mod dp'q'(p' + 2q')/2) for p =Iq and p' even, where d = (p, q), p' = p/d, q' = q/d.